Advances In Nonlinear Programming

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Advances in Nonlinear Programming

Ya-xiang Yuan
Advances in Nonlinear Programming Book PDF

Author : Ya-xiang Yuan
Publisher : Springer Science & Business Media
Page : 353 pages
File Size : 47,5 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461333357

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Advances in Nonlinear Programming by Ya-xiang Yuan Pdf

About 60 scientists and students attended the 96' International Conference on Nonlinear Programming, which was held September 2-5 at Institute of Compu tational Mathematics and Scientific/Engineering Computing (ICMSEC), Chi nese Academy of Sciences, Beijing, China. 25 participants were from outside China and 35 from China. The conference was to celebrate the 60's birthday of Professor M.J.D. Powell (Fellow of Royal Society, University of Cambridge) for his many contributions to nonlinear optimization. On behalf of the Chinese Academy of Sciences, vice president Professor Zhi hong Xu attended the opening ceremony of the conference to express his warm welcome to all the participants. After the opening ceremony, Professor M.J.D. Powell gave the keynote lecture "The use of band matrices for second derivative approximations in trust region methods". 13 other invited lectures on recent advances of nonlinear programming were given during the four day meeting: "Primal-dual methods for nonconvex optimization" by M. H. Wright (SIAM President, Bell Labs), "Interior point trajectories in semidefinite programming" by D. Goldfarb (Columbia University, Editor-in-Chief for Series A of Mathe matical Programming), "An approach to derivative free optimization" by A.

Nonlinear Programming

Mokhtar S. Bazaraa,Hanif D. Sherali,C. M. Shetty
Nonlinear Programming Book PDF

Author : Mokhtar S. Bazaraa,Hanif D. Sherali,C. M. Shetty
Publisher : John Wiley & Sons
Page : 867 pages
File Size : 40,5 Mb
Release : 2013-06-12
Category : Mathematics
ISBN : 9781118626306

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Nonlinear Programming by Mokhtar S. Bazaraa,Hanif D. Sherali,C. M. Shetty Pdf

COMPREHENSIVE COVERAGE OF NONLINEAR PROGRAMMING THEORY AND ALGORITHMS, THOROUGHLY REVISED AND EXPANDED Nonlinear Programming: Theory and Algorithms—now in an extensively updated Third Edition—addresses the problem of optimizing an objective function in the presence of equality and inequality constraints. Many realistic problems cannot be adequately represented as a linear program owing to the nature of the nonlinearity of the objective function and/or the nonlinearity of any constraints. The Third Edition begins with a general introduction to nonlinear programming with illustrative examples and guidelines for model construction. Concentration on the three major parts of nonlinear programming is provided: Convex analysis with discussion of topological properties of convex sets, separation and support of convex sets, polyhedral sets, extreme points and extreme directions of polyhedral sets, and linear programming Optimality conditions and duality with coverage of the nature, interpretation, and value of the classical Fritz John (FJ) and the Karush-Kuhn-Tucker (KKT) optimality conditions; the interrelationships between various proposed constraint qualifications; and Lagrangian duality and saddle point optimality conditions Algorithms and their convergence, with a presentation of algorithms for solving both unconstrained and constrained nonlinear programming problems Important features of the Third Edition include: New topics such as second interior point methods, nonconvex optimization, nondifferentiable optimization, and more Updated discussion and new applications in each chapter Detailed numerical examples and graphical illustrations Essential coverage of modeling and formulating nonlinear programs Simple numerical problems Advanced theoretical exercises The book is a solid reference for professionals as well as a useful text for students in the fields of operations research, management science, industrial engineering, applied mathematics, and also in engineering disciplines that deal with analytical optimization techniques. The logical and self-contained format uniquely covers nonlinear programming techniques with a great depth of information and an abundance of valuable examples and illustrations that showcase the most current advances in nonlinear problems.

High Performance Algorithms and Software for Nonlinear Optimization

Gianni Pillo,Almerico Murli
High Performance Algorithms and Software for Nonlinear Optimization Book PDF

Author : Gianni Pillo,Almerico Murli
Publisher : Springer Science & Business Media
Page : 418 pages
File Size : 44,8 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461302414

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High Performance Algorithms and Software for Nonlinear Optimization by Gianni Pillo,Almerico Murli Pdf

This volume contains the edited texts of the lectures presented at the Workshop on High Performance Algorithms and Software for Nonlinear Optimization held in Erice, Sicily, at the "G. Stampacchia" School of Mathematics of the "E. Majorana" Centre for Scientific Culture, June 30 - July 8, 2001. In the first year of the new century, the aim of the Workshop was to assess the past and to discuss the future of Nonlinear Optimization, and to highlight recent achieve ments and promising research trends in this field. An emphasis was requested on algorithmic and high performance software developments and on new computational experiences, as well as on theoretical advances. We believe that such goal was basically achieved. The Workshop was attended by 71 people from 22 countries. Although not all topics were covered, the presentations gave indeed a wide overview of the field, from different and complementary stand points. Besides the lectures, several formal and informal discussions took place. We wish to express our appreciation for the active contribution of all the participants in the meeting. The 18 papers included in this volume represent a significant selection of the most recent developments in nonlinear programming theory and practice. They show that there is plenty of exciting ideas, implementation issues and new applications which produce a very fast evolution in the field.

Large-Scale Nonlinear Optimization

Gianni Pillo,Massimo Roma
Large Scale Nonlinear Optimization Book PDF

Author : Gianni Pillo,Massimo Roma
Publisher : Springer
Page : 0 pages
File Size : 52,8 Mb
Release : 2011-02-11
Category : Mathematics
ISBN : 1441940146

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Large-Scale Nonlinear Optimization by Gianni Pillo,Massimo Roma Pdf

This book reviews and discusses recent advances in the development of methods and algorithms for nonlinear optimization and its applications, focusing on the large-dimensional case, the current forefront of much research. Individual chapters, contributed by eminent authorities, provide an up-to-date overview of the field from different and complementary standpoints, including theoretical analysis, algorithmic development, implementation issues and applications.

Linear and Nonlinear Optimization

Richard W. Cottle,Mukund N. Thapa
Linear and Nonlinear Optimization Book PDF

Author : Richard W. Cottle,Mukund N. Thapa
Publisher : Springer
Page : 614 pages
File Size : 48,9 Mb
Release : 2017-06-11
Category : Business & Economics
ISBN : 9781493970551

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Linear and Nonlinear Optimization by Richard W. Cottle,Mukund N. Thapa Pdf

​This textbook on Linear and Nonlinear Optimization is intended for graduate and advanced undergraduate students in operations research and related fields. It is both literate and mathematically strong, yet requires no prior course in optimization. As suggested by its title, the book is divided into two parts covering in their individual chapters LP Models and Applications; Linear Equations and Inequalities; The Simplex Algorithm; Simplex Algorithm Continued; Duality and the Dual Simplex Algorithm; Postoptimality Analyses; Computational Considerations; Nonlinear (NLP) Models and Applications; Unconstrained Optimization; Descent Methods; Optimality Conditions; Problems with Linear Constraints; Problems with Nonlinear Constraints; Interior-Point Methods; and an Appendix covering Mathematical Concepts. Each chapter ends with a set of exercises. The book is based on lecture notes the authors have used in numerous optimization courses the authors have taught at Stanford University. It emphasizes modeling and numerical algorithms for optimization with continuous (not integer) variables. The discussion presents the underlying theory without always focusing on formal mathematical proofs (which can be found in cited references). Another feature of this book is its inclusion of cultural and historical matters, most often appearing among the footnotes. "This book is a real gem. The authors do a masterful job of rigorously presenting all of the relevant theory clearly and concisely while managing to avoid unnecessary tedious mathematical details. This is an ideal book for teaching a one or two semester masters-level course in optimization – it broadly covers linear and nonlinear programming effectively balancing modeling, algorithmic theory, computation, implementation, illuminating historical facts, and numerous interesting examples and exercises. Due to the clarity of the exposition, this book also serves as a valuable reference for self-study." Professor Ilan Adler, IEOR Department, UC Berkeley "A carefully crafted introduction to the main elements and applications of mathematical optimization. This volume presents the essential concepts of linear and nonlinear programming in an accessible format filled with anecdotes, examples, and exercises that bring the topic to life. The authors plumb their decades of experience in optimization to provide an enriching layer of historical context. Suitable for advanced undergraduates and masters students in management science, operations research, and related fields." Michael P. Friedlander, IBM Professor of Computer Science, Professor of Mathematics, University of British Columbia

Traces and Emergence of Nonlinear Programming

Giorgio Giorgi,Tinne Hoff Kjeldsen
Traces and Emergence of Nonlinear Programming Book PDF

Author : Giorgio Giorgi,Tinne Hoff Kjeldsen
Publisher : Springer Science & Business Media
Page : 443 pages
File Size : 44,8 Mb
Release : 2013-12-04
Category : Computers
ISBN : 9783034804394

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Traces and Emergence of Nonlinear Programming by Giorgio Giorgi,Tinne Hoff Kjeldsen Pdf

The book contains reproductions of the most important papers that gave birth to the first developments in nonlinear programming. Of particular interest is W. Karush's often quoted Master Thesis, which is published for the first time. The anthology includes an extensive preliminary chapter, where the editors trace out the history of mathematical programming, with special reference to linear and nonlinear programming.​

High Performance Algorithms and Software in Nonlinear Optimization

Renato de Leone,Almerico Murli,Panos M. Pardalos,Gerardo Toraldo
High Performance Algorithms and Software in Nonlinear Optimization Book PDF

Author : Renato de Leone,Almerico Murli,Panos M. Pardalos,Gerardo Toraldo
Publisher : Springer Science & Business Media
Page : 379 pages
File Size : 41,6 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461332794

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High Performance Algorithms and Software in Nonlinear Optimization by Renato de Leone,Almerico Murli,Panos M. Pardalos,Gerardo Toraldo Pdf

This book contains a selection of papers presented at the conference on High Performance Software for Nonlinear Optimization (HPSN097) which was held in Ischia, Italy, in June 1997. The rapid progress of computer technologies, including new parallel architec tures, has stimulated a large amount of research devoted to building software environments and defining algorithms able to fully exploit this new computa tional power. In some sense, numerical analysis has to conform itself to the new tools. The impact of parallel computing in nonlinear optimization, which had a slow start at the beginning, seems now to increase at a fast rate, and it is reasonable to expect an even greater acceleration in the future. As with the first HPSNO conference, the goal of the HPSN097 conference was to supply a broad overview of the more recent developments and trends in nonlinear optimization, emphasizing the algorithmic and high performance software aspects. Bringing together new computational methodologies with theoretical ad vances and new computer technologies is an exciting challenge that involves all scientists willing to develop high performance numerical software. This book contains several important contributions from different and com plementary standpoints. Obviously, the articles in the book do not cover all the areas of the conference topic or all the most recent developments, because of the large number of new theoretical and computational ideas of the last few years.

Recent Advances in Global Optimization

Christodoulos A. Floudas,Panos M. Pardalos
Recent Advances in Global Optimization Book PDF

Author : Christodoulos A. Floudas,Panos M. Pardalos
Publisher : Princeton University Press
Page : 644 pages
File Size : 45,8 Mb
Release : 2014-07-14
Category : Mathematics
ISBN : 9781400862528

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Recent Advances in Global Optimization by Christodoulos A. Floudas,Panos M. Pardalos Pdf

This book will present the papers delivered at the first U.S. conference devoted exclusively to global optimization and will thus provide valuable insights into the significant research on the topic that has been emerging during recent years. Held at Princeton University in May 1991, the conference brought together an interdisciplinary group of the most active developers of algorithms for global optimization in order to focus the attention of the mathematical programming community on the unsolved problems and diverse applications of this field. The main subjects addressed at the conference were advances in deterministic and stochastic methods for global optimization, parallel algorithms for global optimization problems, and applications of global optimization. Although global optimization is primarily a mathematical problem, it is relevant to several other disciplines, including computer science, applied mathematics, physical chemistry, molecular biology, statistics, physics, engineering, operations research, communication theory, and economics. Global optimization problems originate from a wide variety of mathematical models of real-world systems. Some of its applications are allocation and location problems and VLSI and data-base design problems. Originally published in 1991. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming

Mohit Tawarmalani,Nikolaos V. Sahinidis
Convexification and Global Optimization in Continuous and Mixed Integer Nonlinear Programming Book PDF

Author : Mohit Tawarmalani,Nikolaos V. Sahinidis
Publisher : Springer Science & Business Media
Page : 492 pages
File Size : 52,7 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475735321

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Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming by Mohit Tawarmalani,Nikolaos V. Sahinidis Pdf

Interest in constrained optimization originated with the simple linear pro gramming model since it was practical and perhaps the only computationally tractable model at the time. Constrained linear optimization models were soon adopted in numerous application areas and are perhaps the most widely used mathematical models in operations research and management science at the time of this writing. Modelers have, however, found the assumption of linearity to be overly restrictive in expressing the real-world phenomena and problems in economics, finance, business, communication, engineering design, computational biology, and other areas that frequently demand the use of nonlinear expressions and discrete variables in optimization models. Both of these extensions of the linear programming model are NP-hard, thus representing very challenging problems. On the brighter side, recent advances in algorithmic and computing technology make it possible to re visit these problems with the hope of solving practically relevant problems in reasonable amounts of computational time. Initial attempts at solving nonlinear programs concentrated on the de velopment of local optimization methods guaranteeing globality under the assumption of convexity. On the other hand, the integer programming liter ature has concentrated on the development of methods that ensure global optima. The aim of this book is to marry the advancements in solving nonlinear and integer programming models and to develop new results in the more general framework of mixed-integer nonlinear programs (MINLPs) with the goal of devising practically efficient global optimization algorithms for MINLPs.

Applications of Nonlinear Programming to Optimization and Control

H. E. Rauch
Applications of Nonlinear Programming to Optimization and Control Book PDF

Author : H. E. Rauch
Publisher : Elsevier
Page : 156 pages
File Size : 41,9 Mb
Release : 2014-05-23
Category : Mathematics
ISBN : 9781483148397

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Applications of Nonlinear Programming to Optimization and Control by H. E. Rauch Pdf

Applications of Nonlinear Programming to Optimization and Control is a collection of papers presented at the Fourth International Federation of Automatic Control Workshop by the same title, held in San Francisco, California on June 20-21, 1983. This workshop aims to exchange information on the applications of optimization and nonlinear programming techniques to real-life control problems, to investigate ideas that arise from these exchanges, and to look for advances in nonlinear programming that are useful in solving control problems. This book is divided into 16 chapters. It covers a wide range of related topics, starting with computer-aided-design of practical control systems, continuing through advanced work on quasi-Newton methods and gradient restoration algorithms. Other chapters provide specific examples, which apply these methods to representative problems. The remaining chapters present examples, including trajectory optimization, optimal design of a structure for a satellite, identification of hovercraft characteristics, determination of optimal electricity generation, and optimal automatic transmission for road vehicles. This book is of value to computer scientists and mathematicians.

Nonlinear Optimization and Applications

Gianni Pillo,F. Giannessi
Nonlinear Optimization and Applications Book PDF

Author : Gianni Pillo,F. Giannessi
Publisher : Springer Science & Business Media
Page : 367 pages
File Size : 53,7 Mb
Release : 2013-11-11
Category : Computers
ISBN : 9781489902894

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Nonlinear Optimization and Applications by Gianni Pillo,F. Giannessi Pdf

This volume contains the edited texts of the lectures presented at the workshop on Nonlinear Optimization: Theory and Applications, held in Erice at the "G. Stampacchia" School of Mathematics of the "E. Majorana" International Centre for Scientific Culture June 13-21, 1995. The meeting was conceived to review and discuss recent advances and promising research trends concerning theory, algorithms, and innovative applications in the field This is a field of mathematics which is providing viable of Nonlinear Optimization. tools in engineering, in economics and in other applied sciences, and which is giving a great contribution also in the solution of the more practiced linear optimization prob lems. The meeting was attended by approximately 70 people from 18 countries. Besides the lectures, several formal and informal discussions took place. The result was a broad exposure providing a wide and deep understanding of the present research achievements in the field. We wish to express our appreciation for the active contributions of all the partici pants in the meeting. Our gratitude is due to the Ettore Majorana Center in Erice, which offered its facilities and stimulating environment: its staff was certainly instrumental for the success of the meeting. Our gratitude is also due to Francisco Facchinei and Massino Roma for the time spent in the organization of the workshop, and to Giuliana Cai for the careful typesetting of this volume.

Linear and Nonlinear Programming

David G. Luenberger,Yinyu Ye
Linear and Nonlinear Programming Book PDF

Author : David G. Luenberger,Yinyu Ye
Publisher : Springer
Page : 546 pages
File Size : 40,5 Mb
Release : 2015-06-25
Category : Business & Economics
ISBN : 9783319188423

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Linear and Nonlinear Programming by David G. Luenberger,Yinyu Ye Pdf

This new edition covers the central concepts of practical optimization techniques, with an emphasis on methods that are both state-of-the-art and popular. One major insight is the connection between the purely analytical character of an optimization problem and the behavior of algorithms used to solve a problem. This was a major theme of the first edition of this book and the fourth edition expands and further illustrates this relationship. As in the earlier editions, the material in this fourth edition is organized into three separate parts. Part I is a self-contained introduction to linear programming. The presentation in this part is fairly conventional, covering the main elements of the underlying theory of linear programming, many of the most effective numerical algorithms, and many of its important special applications. Part II, which is independent of Part I, covers the theory of unconstrained optimization, including both derivations of the appropriate optimality conditions and an introduction to basic algorithms. This part of the book explores the general properties of algorithms and defines various notions of convergence. Part III extends the concepts developed in the second part to constrained optimization problems. Except for a few isolated sections, this part is also independent of Part I. It is possible to go directly into Parts II and III omitting Part I, and, in fact, the book has been used in this way in many universities. New to this edition is a chapter devoted to Conic Linear Programming, a powerful generalization of Linear Programming. Indeed, many conic structures are possible and useful in a variety of applications. It must be recognized, however, that conic linear programming is an advanced topic, requiring special study. Another important topic is an accelerated steepest descent method that exhibits superior convergence properties, and for this reason, has become quite popular. The proof of the convergence property for both standard and accelerated steepest descent methods are presented in Chapter 8. As in previous editions, end-of-chapter exercises appear for all chapters. From the reviews of the Third Edition: “... this very well-written book is a classic textbook in Optimization. It should be present in the bookcase of each student, researcher, and specialist from the host of disciplines from which practical optimization applications are drawn.” (Jean-Jacques Strodiot, Zentralblatt MATH, Vol. 1207, 2011)

Nonlinear Optimization and Related Topics

Gianni Pillo,F. Giannessi
Nonlinear Optimization and Related Topics Book PDF

Author : Gianni Pillo,F. Giannessi
Publisher : Springer Science & Business Media
Page : 484 pages
File Size : 49,6 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475732269

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Nonlinear Optimization and Related Topics by Gianni Pillo,F. Giannessi Pdf

This volume contains the edited texts of the lectures presented at the Workshop on Nonlinear Optimization held in Erice, Sicily, at the "G. Stampacchia" School of Mathematics of the "E. Majorana" Centre for Scientific Culture, June 23 -July 2, 1998. In the tradition of these meetings, the main purpose was to review and discuss recent advances and promising research trends concerning theory, algorithms and innovative applications in the field of Nonlinear Optimization, and of related topics such as Convex Optimization, Nonsmooth Optimization, Variational Inequalities and Complementarity Problems. The meeting was attended by 83 people from 21 countries. Besides the lectures, several formal and informal discussions took place. The result was a wide and deep knowledge of the present research tendencies in the field. We wish to express our appreciation for the active contribution of all the par ticipants in the meeting. Our gratitude is due to the Ettore Majorana Centre in Erice, which offered its facilities and rewarding environment: its staff was certainly instrumental for the success of the meeting. Our gratitude is also due to Francisco Facchinei and Massimo Roma for the effort and time devoted as members of the Organising Committee. We are indebted to the Italian National Research Council, and in particular to the Group on Functional Analysis and its Applications and to the Committees on Engineering Sciences and on Information Sciences and Technolo gies for their financial support. Finally, we address our thanks to Kluwer Academic Publishers for having offered to publish this volume.

Practical Methods for Optimal Control Using Nonlinear Programming, Third Edition

John T. Betts
Practical Methods for Optimal Control Using Nonlinear Programming Third Edition Book PDF

Author : John T. Betts
Publisher : SIAM
Page : 748 pages
File Size : 43,8 Mb
Release : 2020-07-09
Category : Mathematics
ISBN : 9781611976199

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Practical Methods for Optimal Control Using Nonlinear Programming, Third Edition by John T. Betts Pdf

How do you fly an airplane from one point to another as fast as possible? What is the best way to administer a vaccine to fight the harmful effects of disease? What is the most efficient way to produce a chemical substance? This book presents practical methods for solving real optimal control problems such as these. Practical Methods for Optimal Control Using Nonlinear Programming, Third Edition focuses on the direct transcription method for optimal control. It features a summary of relevant material in constrained optimization, including nonlinear programming; discretization techniques appropriate for ordinary differential equations and differential-algebraic equations; and several examples and descriptions of computational algorithm formulations that implement this discretize-then-optimize strategy. The third edition has been thoroughly updated and includes new material on implicit Runge–Kutta discretization techniques, new chapters on partial differential equations and delay equations, and more than 70 test problems and open source FORTRAN code for all of the problems. This book will be valuable for academic and industrial research and development in optimal control theory and applications. It is appropriate as a primary or supplementary text for advanced undergraduate and graduate students.

The Mathematics of Nonlinear Programming

Anthony L. Peressini,Francis E. Sullivan,J.J. Jr. Uhl
The Mathematics of Nonlinear Programming Book PDF

Author : Anthony L. Peressini,Francis E. Sullivan,J.J. Jr. Uhl
Publisher : Springer
Page : 0 pages
File Size : 51,8 Mb
Release : 2012-09-30
Category : Mathematics
ISBN : 146126989X

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The Mathematics of Nonlinear Programming by Anthony L. Peressini,Francis E. Sullivan,J.J. Jr. Uhl Pdf

Nonlinear programming provides an excellent opportunity to explore an interesting variety of pure and solidly applicable mathematics, numerical analysis, and computing. This text develops some of the ideas and techniques involved in the optimization methods using calculus, leading to the study of convexity. This is followed by material on basic numerical methods, least squares, the Karush-Kuhn-Tucker theorem, penalty functions, and Lagrange multipliers. The authors have aimed their presentation at the student who has a working knowledge of matrix algebra and advanced calculus, but has had no previous exposure to optimization.