In combinatorial optimization, there are numerous computationally hard problems
arising in real world applications, such as ... We focus on the mathematical theory of optimization, especially, various convergence problems in nonlinear ...

Author: Ding-Zhu Du

Publisher: Springer Science & Business Media

ISBN: 9781475757958

Category: Mathematics

Page: 273

View: 377

This book provides an introduction to the mathematical theory of optimization. It emphasizes the convergence theory of nonlinear optimization algorithms and applications of nonlinear optimization to combinatorial optimization. Mathematical Theory of Optimization includes recent developments in global convergence, the Powell conjecture, semidefinite programming, and relaxation techniques for designs of approximation solutions of combinatorial optimization problems.

Math. Soc. 3, 1952, 170-174. G. S. Goodman, The duality of convex functions and
Cesari's property (Q). J. Optimization Theory Appl. 19, 1976, 17-23. J. Henry,
Étude de la controllabilité de certaines equations paraboliques non-lineaires,
Proc.

Then, applying stochastic realization theory and the bounded real lemma we
derive alternative expressions for the cost function. ... A. Rantzer, C.I. Byrnes (Eds
.): Directions in Mathematical Systems Theory and Optimization, LNCIS 286, pp.

Author: Anders Rantzer

Publisher: Springer Science & Business Media

ISBN: 9783540000655

Category: Computers

Page: 391

View: 554

For more than three decades, Anders Lindquist has delivered fundamental cont- butions to the ?elds of systems, signals and control. Throughout this period, four themes can perhaps characterize his interests: Modeling, estimation and ?ltering, feedback and robust control. His contributions to modeling include seminal work on the role of splitting subspaces in stochastic realization theory, on the partial realization problem for both deterministic and stochastic systems, on the solution of the rational covariance extension problem and on system identi?cation. His contributions to ?ltering and estimation include the development of fast ?ltering algorithms, leading to a nonlinear dynamical system which computes spectral factors in its steady state, and which provide an alternate, linear in the dimension of the state space, to computing the Kalman gain from a matrix Riccati equation. His further research on the phase portrait of this dynamical system gave a better understanding of when the Kalman ?lter will converge, answering an open question raised by Kalman. While still a student he established the separation principle for stochastic function differential equations, including some fundamental work on optimal control for stochastic systems with time lags. He continued his interest in feedback control by deriving optimal and robust control feedback laws for suppressing the effects of harmonic disturbances. Moreover, his recent work on a complete parameterization of all rational solutions to the Nevanlinna-Pick problem is providing a new approach to robust control design.

Author: Michael D. IntriligatorPublish On: 2002-01-01

BIBLIOGRAPHY Balakrishnan, A. V., and L. W. Neustadt, eds., Mathematical Theory of Control. New York: Academic Press, Inc., 1967. Berkovitz, L. D., “A
Variational Approach to Differential Games,” in Advances in Game Theory,
Annals of ...

Author: Michael D. Intriligator

Publisher: SIAM

ISBN: 9780898715118

Category: Mathematics

Page: 508

View: 585

A classic account of mathematical programming and control techniques and their applications to static and dynamic problems in economics.

Definitive work draws on game theory, calculus of variations, and control theory to solve an array of problems: military, pursuit and evasion, athletic contests, many more. Detailed examples, formal calculations. 1965 edition.

... Approaches to Mathematical Problems * PLANE AND MCMILLAN , Discrete Optimization : Integer Programming and ... and Fundamentals SCHAEFER , A Mathematical Theory of Global Program Optimization SCHULTZ , Spline Analysis
...

Solitons in Mathematics and Physics PRANAB KUMAR SEN, Theory and
Applications of Sequential Nonparametrics ... in the Neurosciences FRANK H.
CLARKE, Methods of Dynamic and Nonsmooth Optimization ROBERT B.
GARDNER, The ...

Author: Peter D. Lax

Publisher: SIAM

ISBN: 1611970563

Category: Conservation laws (Mathematics)

Page: 48

View: 778

This book deals with the mathematical side of the theory of shock waves. The author presents what is known about the existence and uniqueness of generalized solutions of the initial value problem subject to the entropy conditions. The subtle dissipation introduced by the entropy condition is investigated and the slow decay in signal strength it causes is shown.

Expected Utility In a formal sense , the theory of optimization under uncertainty
does not require any new mathematical theory as such . The choice variables
lead to random outcomes with objective or subjective probability distributions .

Author: Avinash K. Dixit

Publisher: Oxford University Press on Demand

ISBN: 0198772106

Category: Business & Economics

Page: 188

View: 665

A new edition of a student text which provides a broad study of optimization methods. It builds on the base of simple economic theory, elementary linear algebra and calculus, and reinforces each new mathematical idea by relating it to its economic application.

Mathematical optimization theory provides a better alternative for decision
making in these situations provided one can represent the decisions and the
system mathematically. With the advent of computers it is possible to exploit
these theories ...

Author: Urmila Diwekar

Publisher: Springer Science & Business Media

ISBN: 9780387766355

Category: Mathematics

Page: 291

View: 337

Provides well-written self-contained chapters, including problem sets and exercises, making it ideal for the classroom setting; Introduces applied optimization to the hazardous waste blending problem; Explores linear programming, nonlinear programming, discrete optimization, global optimization, optimization under uncertainty, multi-objective optimization, optimal control and stochastic optimal control; Includes an extensive bibliography at the end of each chapter and an index; GAMS files of case studies for Chapters 2, 3, 4, 5, and 7 are linked to http://www.springer.com/math/book/978-0-387-76634-8; Solutions manual available upon adoptions.

This book presents a coherent and systematic exposition of the mathematical theory of the problems of optimization and stability. Both of these are topics
central to economic analysis since the latter is so much concerned with the optimizing ...

Author: Brian Beavis

Publisher: Cambridge University Press

ISBN: 0521336058

Category: Business & Economics

Page: 414

View: 525

This book presents a coherent and systematic exposition of the mathematical theory of the problems of optimization and stability. Both of these are topics central to economic analysis since the latter is so much concerned with the optimizing behaviour of economic agents and the stability of the interaction processes to which this gives rise. The topics covered include convexity, mathematical programming, fixed point theorems, comparative static analysis and duality, the stability of dynamic systems, the calculus of variations and optimal control theory. The authors present a more detailed and wide-ranging discussion of these topics than is to be found in the few books which attempt a similar coverage. Although the text deals with fairly advanced material, the mathematical prerequisites are minimised by the inclusion of an integrated mathematical review designed to make the text self-contained and accessible to the reader with only an elementary knowledge of calculus and linear algebra. A novel feature of the book is that it provides the reader with an understanding and feel for the kinds of mathematical techniques most useful for dealing with particular economic problems. This is achieved through an extensive use of a broad range of economic examples (rather than the numerical/algebraic examples so often found).This is suitable for use in advanced undergraduate and postgraduate courses in economic analysis and should in addition prove a useful reference work for practising economists.

As with the three preceding volumes, all the material contained with the 42 sections of this volume is made easily accessible by way of numerous examples, both concrete and abstract in nature.

Author: L.S. Pontryagin

Publisher: CRC Press

ISBN: 2881240771

Category: Mathematics

Page: 360

View: 665

The fourth and final volume in this comprehensive set presents the maximum principle as a wide ranging solution to nonclassical, variational problems. This one mathematical method can be applied in a variety of situations, including linear equations with variable coefficients, optimal processes with delay, and the jump condition. As with the three preceding volumes, all the material contained with the 42 sections of this volume is made easily accessible by way of numerous examples, both concrete and abstract in nature.

1.1.1 EVOLUTION OF MATHEMATICAL THEORIES AND ALGORITHMS In1947,
GeorgeDantziginvented thesimplexalgorithmforlinearprogramming,1oneofthefun-
damental building blocks of mathematical optimization. Since then, the field of ...

Author: Karu Sankaralingam

Publisher: Morgan & Claypool Publishers

ISBN: 9781627052108

Category: Computers

Page: 144

View: 846

In this book we give an overview of modeling techniques used to describe computer systems to mathematical optimization tools. We give a brief introduction to various classes of mathematical optimization frameworks with special focus on mixed integer linear programming which provides a good balance between solver time and expressiveness. We present four detailed case studies -- instruction set customization, data center resource management, spatial architecture scheduling, and resource allocation in tiled architectures -- showing how MILP can be used and quantifying by how much it outperforms traditional design exploration techniques. This book should help a skilled systems designer to learn techniques for using MILP in their problems, and the skilled optimization expert to understand the types of computer systems problems that MILP can be applied to.

This may serve to explain why there has been an enduring symbiosis between mathematical theories of optimization and the applications of mathematics, even
though the forms of the problems (the “paradigms”) being considered evolve in ...

Author: Frank H. Clarke

Publisher: SIAM

ISBN: 9780898712568

Category: Mathematics

Page: 308

View: 981

Mathematical Reviews said of this book that it was 'destined to become a classical reference.' This book has appeared in Russian translation and has been praised both for its lively exposition and its fundamental contributions. The author first develops a general theory of nonsmooth analysis and geometry which, together with a set of associated techniques, has had a profound effect on several branches of analysis and optimization. Clarke then applies these methods to obtain a powerful, unified approach to the analysis of problems in optimal control and mathematical programming. Examples are drawn from economics, engineering, mathematical physics, and various branches of analysis in this reprint volume.

Optimal Control: An Introduction to the Theory and Its Applications. McGraw-Hill,
New York. Bellman, R. (1957). Dynamic Programming. Princeton Univ. Press,
Princeton. Bellman, R. (1967). Introduction to the Mathematical Theory of Control
...

Author: Yasuo Murata

Publisher: Academic Press

ISBN: 9781483271293

Category: Business & Economics

Page: 438

View: 191

Economic Theory and Mathematical Economics: Mathematics for Stability and Optimization of Economic Systems provides information pertinent to the stability aspects and optimization methods relevant to various economic systems. This book presents relevant mathematical theorems sufficient to develop important economic systems, including Leontief input–output systems, Keynesian dynamic models, the Ramsey optimal accumulation systems, and von Neumann expanding economic systems. Organized into two parts encompassing nine chapters, this book begins with an overview of useful theorems on matrices, eigenvalue problems, and matrices with dominant diagonals and P-matrices. This text then explores the linear transformations on vector spaces. Other chapters consider the Hawkins–Simon theorem concerning non-negative linear systems. This book discusses as well the dual linear relations and optimization methods applicable to inequality economic systems. The final chapter deals with powerful optimal control method for dynamical systems. This book is a valuable resource for mathematicians, economists, research workers, and graduate students.

Journal of Research of the National Bureau of Standards, Section B, Mathematics
and Mathematical Physics, 70B, 211–218, July–Sept. 1966. [7.76] Nemhauser,
G. L. ... The Mathematical Theory of Optimal Processes. (Authorized Translation ...

Author: Donald A. Pierre

Publisher: Courier Corporation

ISBN: 9780486136950

Category: Mathematics

Page: 640

View: 821

Broad-spectrum approach to important topic. Explores the classic theory of minima and maxima, classical calculus of variations, simplex technique and linear programming, optimality and dynamic programming, more. 1969 edition.

Optimization has been expanding in all directions at an astonishing rate during
the last few decades. ... developed calculus of variations and the theory of
stationary values lie in the foundation of the modern mathematical theory of optimization.

Author: Godfrey C. Onwubolu

Publisher: Springer Science & Business Media

ISBN: 354020167X

Category: Business & Economics

Page: 712

View: 902

Presently, general-purpose optimization techniques such as Simulated Annealing, and Genetic Algorithms, have become standard optimization techniques. Concerted research efforts have been made recently in order to invent novel optimization techniques for solving real life problems, which have the attributes of memory update and population-based search solutions. The book describes a variety of these novel optimization techniques which in most cases outperform the standard optimization techniques in many application areas. New Optimization Techniques in Engineering reports applications and results of the novel optimization techniques considering a multitude of practical problems in the different engineering disciplines – presenting both the background of the subject area and the techniques for solving the problems.

CHAPTER 6 Redundancy Optimization 1. INTRODUCTION In this chapter we
present models concerned with optimization of redundancy. The first problem
treated, that of maximizing the reliability of a series system subject to one or more
...

Author: Richard E. Barlow

Publisher: SIAM

ISBN: 1611971195

Category: Mathematical statistics

Page: 258

View: 620

This monograph presents a survey of mathematical models useful in solving reliability problems. It includes a detailed discussion of life distributions corresponding to wearout and their use in determining maintenance policies, and covers important topics such as the theory of increasing (decreasing) failure rate distributions, optimum maintenance policies, and the theory of coherent systems. The emphasis throughout the book is on making minimal assumptions--and only those based on plausible physical considerations--so that the resulting mathematical deductions may be safely made about a large variety of commonly occurring reliability situations. The first part of the book is concerned with component reliability, while the second part covers system reliability, including problems that are as important today as they were in the 1960s. Mathematical reliability refers to a body of ideas, mathematical models, and methods directed toward the solution of problems in predicting, estimating, or optimizing the probability of survival, mean life, or, more generally, life distribution of components and systems. The enduring relevance of the subject of reliability and the continuing demand for a graduate-level book on this topic are the driving forces behind its republication. Unavailable since its original publication in 1965, Mathematical Theory of Reliability now joins a growing list of volumes in SIAM's Classics series. Although contemporary reliability books are now available, few provide as mathematically rigorous a treatment of the required probability background as this one.

2000 ISBN 0-7923-6323-X R.G. Strongin and Y.D. Sergeyev: Global Optimization
with Non-Convex Constraints. 2000 ISBN ... 2001 ISBN 0-7923-7144-5 D.-Z. Du,
P.M. Pardalos and W. Wu: Mathematical Theory of Optimization. 2001 ISBN ...

Author: Diethard Klatte

Publisher: Springer Science & Business Media

ISBN: 9781402005503

Category: Mathematics

Page: 329

View: 697

The book establishes links between regularity and derivative concepts of nonsmooth analysis and studies of solution methods and stability for optimization, complementarity and equilibrium problems. In developing necessary tools, it presents, in particular: an extended analysis of Lipschitz functions and the calculus of their generalized derivatives, including regularity, successive approximation and implicit functions for multivalued mappings; a unified theory of Lipschitzian critical points in optimization and other variational problems, with relations to reformulations by penalty, barrier and NCP functions; an analysis of generalized Newton methods based on linear and nonlinear approximations; the interpretation of hypotheses, generalized derivatives and solution methods in terms of original data and quadratic approximations; a rich collection of instructive examples and exercises.£/LIST£ Audience: Researchers, graduate students and practitioners in various fields of applied mathematics, engineering, OR and economics. Also university teachers and advanced students who wish to get insights into problems, future directions and recent developments.

Introduction In mathematics the Soviet Union and the United States lead the
world and are at approximately the same level [ 1 ] . In the mathematical theory of
control and stability , Soviet mathematicians have worked longer and harder than
...

This book presents the mathematical theory of vector variational inequalities and their relations with vector optimization problems.

Author: Qamrul Hasan Ansari

Publisher: Springer

ISBN: 3319630482

Category: Business & Economics

Page: 509

View: 260

This book presents the mathematical theory of vector variational inequalities and their relations with vector optimization problems. It is the first-ever book to introduce well-posedness and sensitivity analysis for vector equilibrium problems. The first chapter provides basic notations and results from the areas of convex analysis, functional analysis, set-valued analysis and fixed-point theory for set-valued maps, as well as a brief introduction to variational inequalities and equilibrium problems. Chapter 2 presents an overview of analysis over cones, including continuity and convexity of vector-valued functions. The book then shifts its focus to solution concepts and classical methods in vector optimization. It describes the formulation of vector variational inequalities and their applications to vector optimization, followed by separate chapters on linear scalarization, nonsmooth and generalized vector variational inequalities. Lastly, the book introduces readers to vector equilibrium problems and generalized vector equilibrium problems. Written in an illustrative and reader-friendly way, the book offers a valuable resource for all researchers whose work involves optimization and vector optimization.