Download or read book Theory of Duality in Mathematical Programming written by Manfred Walk and published by Springer. This book was released on 1989 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Generalized Convexity Generalized Monotonicity Recent Results written by Jean-Pierre Crouzeix and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: A function is convex if its epigraph is convex. This geometrical structure has very strong implications in terms of continuity and differentiability. Separation theorems lead to optimality conditions and duality for convex problems. A function is quasiconvex if its lower level sets are convex. Here again, the geo metrical structure of the level sets implies some continuity and differentiability properties for quasiconvex functions. Optimality conditions and duality can be derived for optimization problems involving such functions as well. Over a period of about fifty years, quasiconvex and other generalized convex functions have been considered in a variety of fields including economies, man agement science, engineering, probability and applied sciences in accordance with the need of particular applications. During the last twenty-five years, an increase of research activities in this field has been witnessed. More recently generalized monotonicity of maps has been studied. It relates to generalized convexity off unctions as monotonicity relates to convexity. Generalized monotonicity plays a role in variational inequality problems, complementarity problems and more generally, in equilibrium prob lems.

Download or read book Mathematical Programs with Equilibrium Constraints written by Zhi-Quan Luo and published by Cambridge University Press. This book was released on 1996-11-13 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: An extensive study for an important class of constrained optimisation problems known as Mathematical Programs with Equilibrium Constraints.

Download or read book Convex Duality and Financial Mathematics written by Peter Carr and published by Springer. This book was released on 2018-07-18 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a concise introduction to convex duality in financial mathematics. Convex duality plays an essential role in dealing with financial problems and involves maximizing concave utility functions and minimizing convex risk measures. Recently, convex and generalized convex dualities have shown to be crucial in the process of the dynamic hedging of contingent claims. Common underlying principles and connections between different perspectives are developed; results are illustrated through graphs and explained heuristically. This book can be used as a reference and is aimed toward graduate students, researchers and practitioners in mathematics, finance, economics, and optimization. Topics include: Markowitz portfolio theory, growth portfolio theory, fundamental theorem of asset pricing emphasizing the duality between utility optimization and pricing by martingale measures, risk measures and its dual representation, hedging and super-hedging and its relationship with linear programming duality and the duality relationship in dynamic hedging of contingent claims

Download or read book Duality in Mathematical Programming written by Stepan Karamardian and published by . This book was released on 1966 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Conjugate Duality and Optimization written by R. Tyrrell Rockafellar and published by SIAM. This book was released on 1974-01-01 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a relatively brief introduction to conjugate duality in both finite- and infinite-dimensional problems. An emphasis is placed on the fundamental importance of the concepts of Lagrangian function, saddle-point, and saddle-value. General examples are drawn from nonlinear programming, approximation, stochastic programming, the calculus of variations, and optimal control.

Download or read book Conjugate Duality in Convex Optimization written by Radu Ioan Bot and published by Springer Science & Business Media. This book was released on 2009-12-24 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: The results presented in this book originate from the last decade research work of the author in the ?eld of duality theory in convex optimization. The reputation of duality in the optimization theory comes mainly from the major role that it plays in formulating necessary and suf?cient optimality conditions and, consequently, in generatingdifferent algorithmic approachesfor solving mathematical programming problems. The investigations made in this work prove the importance of the duality theory beyond these aspects and emphasize its strong connections with different topics in convex analysis, nonlinear analysis, functional analysis and in the theory of monotone operators. The ?rst part of the book brings to the attention of the reader the perturbation approach as a fundamental tool for developing the so-called conjugate duality t- ory. The classical Lagrange and Fenchel duality approaches are particular instances of this general concept. More than that, the generalized interior point regularity conditions stated in the past for the two mentioned situations turn out to be p- ticularizations of the ones given in this general setting. In our investigations, the perturbationapproachrepresentsthestartingpointforderivingnewdualityconcepts for several classes of convex optimization problems. Moreover, via this approach, generalized Moreau–Rockafellar formulae are provided and, in connection with them, a new class of regularity conditions, called closedness-type conditions, for both stable strong duality and strong duality is introduced. By stable strong duality we understand the situation in which strong duality still holds whenever perturbing the objective function of the primal problem with a linear continuous functional.

Download or read book Linear Programming with MATLAB written by Michael C. Ferris and published by SIAM. This book was released on 2007-01-01 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained introduction to linear programming using MATLAB® software to elucidate the development of algorithms and theory. Exercises are included in each chapter, and additional information is provided in two appendices and an accompanying Web site. Only a basic knowledge of linear algebra and calculus is required.

Download or read book Applied Mathematical Programming written by Stephen P. Bradley and published by Addison Wesley Publishing Company. This book was released on 1977 with total page 748 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical programming: an overview; solving linear programs; sensitivity analysis; duality in linear programming; mathematical programming in practice; integration of strategic and tactical planning in the aluminum industry; planning the mission and composition of the U.S. merchant Marine fleet; network models; integer programming; design of a naval tender job shop; dynamic programming; large-scale systems; nonlinear programming; a system for bank portfolio planning; vectors and matrices; linear programming in matrix form; a labeling algorithm for the maximun-flow network problem.

Download or read book Extremal Methods and Systems Analysis written by A. V. Fiacco and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers appearing in this Volume were selected from a collec tion of papers presented at the Internationa~ Symposium on Extrema~ Methods and Systems Ana~ysis on the Occasion of Professor A. Charnes' 60th Birthday, at the University of Texas in Austin, 13-15 September 1977. As coeditors, we have followed the normal editorial procedures of scholarly journals. We have obtained invaluable assistance from a number of colleagues who essentially performed the duties of associate editors, coordinating most of the reviews. All papers except those appearing in the Historica~ Perspectives section were refereed by at least two individuals with competency in the respective area. Because of the wide range and diversity of the topics, it would have been im possible for us to make a consistently rational selection of papers without the help of the associate editors and referees. We are indeed grateful to them. The breadth of extremal methods and systems analysis, suggested by the range of topics covered in these papers, is characteristic of the field and also of the scholarly work of Professor Charnes. Extre mal methods and systems analysis has been a pioneering and systematic approach to the development and application of new scientific theories and methods for problems of management and operations in both the pri vate and public sectors, spanning all major disciplines from economics to engineering.

Download or read book Convexity and Duality in Optimization written by Jacob Ponstein and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: The analysis and optimization of convex functions have re ceived a great deal of attention during the last two decades. If we had to choose two key-words from these developments, we would retain the concept of ~ubdi66~e~ and the duality theo~y. As it usual in the development of mathematical theories, people had since tried to extend the known defi nitions and properties to new classes of functions, including the convex ones. For what concerns the generalization of the notion of subdifferential, tremendous achievements have been carried out in the past decade and any rna·· thematician who is faced with a nondifferentiable nonconvex function has now a panoply of generalized subdifferentials or derivatives at his disposal. A lot remains to be done in this area, especially concerning vecto~-valued functions ; however we think the golden age for these researches is behind us. Duality theory has also fascinated many mathematicians since the underlying mathematical framework has been laid down in the context of Convex Analysis. The various duality schemes which have emerged in the re cent years, despite of their mathematical elegance, have not always proved as powerful as expected.

Download or read book Asymptotic Duality in Mathematical Programming and Duality in Markov Programs written by John Parkhill Evans and published by . This book was released on 1968 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Duality in Mathematical Programming written by Ricardo A. Mitchell and published by . This book was released on 1984 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Linear Optimization and Duality written by Craig A. Tovey and published by CRC Press. This book was released on 2020-12-15 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear Optimization and Dualiyy: A Modern Exposition departs from convention in significant ways. Standard linear programming textbooks present the material in the order in which it was discovered. Duality is treated as a difficult add-on after coverage of formulation, the simplex method, and polyhedral theory. Students end up without knowing duality in their bones. This text brings in duality in Chapter 1 and carries duality all the way through the exposition. Chapter 1 gives a general definition of duality that shows the dual aspects of a matrix as a column of rows and a row of columns. The proof of weak duality in Chapter 2 is shown via the Lagrangian, which relies on matrix duality. The first three LP formulation examples in Chapter 3 are classic primal-dual pairs including the diet problem and 2-person zero sum games. For many engineering students, optimization is their first immersion in rigorous mathematics. Conventional texts assume a level of mathematical sophistication they don’t have. This text embeds dozens of reading tips and hundreds of answered questions to guide such students. Features Emphasis on duality throughout Practical tips for modeling and computation Coverage of computational complexity and data structures Exercises and problems based on the learning theory concept of the zone of proximal development Guidance for the mathematically unsophisticated reader About the Author Craig A. Tovey is a professor in the H. Milton Stewart School of Industrial and Systems Engineering at Georgia Institute of Technology. Dr. Tovey received an AB from Harvard College, an MS in computer science and a PhD in operations research from Stanford University. His principal activities are in operations research and its interdisciplinary applications. He received a Presidential Young Investigator Award and the Jacob Wolfowitz Prize for research in heuristics. He was named an Institute Fellow at Georgia Tech, and was recognized by the ACM Special Interest Group on Electronic Commerce with the Test of Time Award. Dr. Tovey received the 2016 Golden Goose Award for his research on bee foraging behavior leading to the development of the Honey Bee Algorithm.

Download or read book A New Duality Theory for Mathematical Programming written by B. F. Svaiter and published by . This book was released on 1994 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Linear Programming Duality written by Achim Bachem and published by Springer Science & Business Media. This book was released on 1992-07-30 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main theorem of Linear Programming Duality, relating a "pri- mal" Linear Programming problem to its "dual" and vice versa, can be seen as a statement about sign patterns of vectors in complemen- tary subspaces of Rn. This observation, first made by R.T. Rockafellar in the late six- ties, led to the introduction of certain systems of sign vectors, called "oriented matroids." Indeed, when oriented matroids came into being in the early seventies, one of the main issues was to study the fun- damental principles underlying Linear Progra.mrning Duality in this abstract setting. In the present book we tried to follow this approach, i.e., rather than starting out from ordinary (unoriented) matroid theory, we pre- ferred to develop oriented matroids directly as appropriate abstrac- tions of linear subspaces. Thus, the way we introduce oriented ma- troids makes clear that these structures are the most general -and hence, the most simple -ones in which Linear Programming Duality results can be stated and proved. We hope that this helps to get a better understanding of LP-Duality for those who have learned about it before und a good introduction for those who have not.

Download or read book Duality in Optimization and Variational Inequalities written by C.j. Goh and published by CRC Press. This book was released on 2002-05-10 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive volume covers a wide range of duality topics ranging from simple ideas in network flows to complex issues in non-convex optimization and multicriteria problems. In addition, it examines duality in the context of variational inequalities and vector variational inequalities, as generalizations to optimization. Duality in Optimizati