Download or read book Conditions for Finite Convergence of Algorithms for Nonlinear Programs and Variational Inequalities written by Faiz Abdullah Al-Khayyal and published by . This book was released on 1988 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algorithms for nonlinear programming and variational inequality problems are, in general, only guaranteed to converge in the limit to a Karush-Kuhn-Tucker point, in the case of nonlinear programs, or a solution in the case of variational inequalities. In this paper we derive sufficient conditions for nonlinear programs and variational inequalities such that any convergent algorithm can be modified to guarantee finite convergence to a solution. Our conditions are more general than existing results and, in addition, have wider applicability. Moreover, we note that our sufficient conditions are close to the related necessary conditions, and show by counterexamples that our main nondegeneracy assumptions cannot be relaxed. Keywords: Convergence of algorithms; Nonlinear programs; Variational inequalities.
Download or read book Nonlinear Programming and Variational Inequality Problems written by Michael Patriksson and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since I started working in the area of nonlinear programming and, later on, variational inequality problems, I have frequently been surprised to find that many algorithms, however scattered in numerous journals, monographs and books, and described rather differently, are closely related to each other. This book is meant to help the reader understand and relate algorithms to each other in some intuitive fashion, and represents, in this respect, a consolidation of the field. The framework of algorithms presented in this book is called Cost Approxi mation. (The preface of the Ph.D. thesis [Pat93d] explains the background to the work that lead to the thesis, and ultimately to this book.) It describes, for a given formulation of a variational inequality or nonlinear programming problem, an algorithm by means of approximating mappings and problems, a principle for the update of the iteration points, and a merit function which guides and monitors the convergence of the algorithm. One purpose of this book is to offer this framework as an intuitively appeal ing tool for describing an algorithm. One of the advantages of the framework, or any reasonable framework for that matter, is that two algorithms may be easily related and compared through its use. This framework is particular in that it covers a vast number of methods, while still being fairly detailed; the level of abstraction is in fact the same as that of the original problem statement.
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1989 with total page 988 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Optimal Quadratic Programming Algorithms written by Zdenek Dostál and published by Springer Science & Business Media. This book was released on 2009-04-03 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quadratic programming (QP) is one advanced mathematical technique that allows for the optimization of a quadratic function in several variables in the presence of linear constraints. This book presents recently developed algorithms for solving large QP problems and focuses on algorithms which are, in a sense optimal, i.e., they can solve important classes of problems at a cost proportional to the number of unknowns. For each algorithm presented, the book details its classical predecessor, describes its drawbacks, introduces modifications that improve its performance, and demonstrates these improvements through numerical experiments. This self-contained monograph can serve as an introductory text on quadratic programming for graduate students and researchers. Additionally, since the solution of many nonlinear problems can be reduced to the solution of a sequence of QP problems, it can also be used as a convenient introduction to nonlinear programming.
Download or read book Finite Dimensional Variational Inequalities and Complementarity Problems written by Francisco Facchinei and published by Springer Science & Business Media. This book was released on 2007-06-04 with total page 698 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is part two of a two-volume work presenting a comprehensive treatment of the finite-dimensional variational inequality and complementarity problem. It details algorithms for solving finite dimensional variational inequalities and complementarity problems. Coverage includes abundant exercises as well as an extensive bibliography. The book will be an enduring reference on the subject and provide the foundation for its sustained growth.
Download or read book Optimization written by Elijah Polak and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 801 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with optimality conditions, algorithms, and discretization tech niques for nonlinear programming, semi-infinite optimization, and optimal con trol problems. The unifying thread in the presentation consists of an abstract theory, within which optimality conditions are expressed in the form of zeros of optimality junctions, algorithms are characterized by point-to-set iteration maps, and all the numerical approximations required in the solution of semi-infinite optimization and optimal control problems are treated within the context of con sistent approximations and algorithm implementation techniques. Traditionally, necessary optimality conditions for optimization problems are presented in Lagrange, F. John, or Karush-Kuhn-Tucker multiplier forms, with gradients used for smooth problems and subgradients for nonsmooth prob lems. We present these classical optimality conditions and show that they are satisfied at a point if and only if this point is a zero of an upper semicontinuous optimality junction. The use of optimality functions has several advantages. First, optimality functions can be used in an abstract study of optimization algo rithms. Second, many optimization algorithms can be shown to use search directions that are obtained in evaluating optimality functions, thus establishing a clear relationship between optimality conditions and algorithms. Third, estab lishing optimality conditions for highly complex problems, such as optimal con trol problems with control and trajectory constraints, is much easier in terms of optimality functions than in the classical manner. In addition, the relationship between optimality conditions for finite-dimensional problems and semi-infinite optimization and optimal control problems becomes transparent.
Download or read book Optimality Conditions in Convex Optimization written by Anulekha Dhara and published by CRC Press. This book was released on 2011-10-17 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimality Conditions in Convex Optimization explores an important and central issue in the field of convex optimization: optimality conditions. It brings together the most important and recent results in this area that have been scattered in the literature—notably in the area of convex analysis—essential in developing many of the important results in this book, and not usually found in conventional texts. Unlike other books on convex optimization, which usually discuss algorithms along with some basic theory, the sole focus of this book is on fundamental and advanced convex optimization theory. Although many results presented in the book can also be proved in infinite dimensions, the authors focus on finite dimensions to allow for much deeper results and a better understanding of the structures involved in a convex optimization problem. They address semi-infinite optimization problems; approximate solution concepts of convex optimization problems; and some classes of non-convex problems which can be studied using the tools of convex analysis. They include examples wherever needed, provide details of major results, and discuss proofs of the main results.
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 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a solid foundation and an extensive study for an important class of constrained optimization problems known as Mathematical Programs with Equilibrium Constraints (MPEC), which are extensions of bilevel optimization problems. The book begins with the description of many source problems arising from engineering and economics that are amenable to treatment by the MPEC methodology. Error bounds and parametric analysis are the main tools to establish a theory of exact penalisation, a set of MPEC constraint qualifications and the first-order and second-order optimality conditions. The book also describes several iterative algorithms such as a penalty-based interior point algorithm, an implicit programming algorithm and a piecewise sequential quadratic programming algorithm for MPECs. Results in the book are expected to have significant impacts in such disciplines as engineering design, economics and game equilibria, and transportation planning, within all of which MPEC has a central role to play in the modelling of many practical problems.
Download or read book Convergence Conditions for Nonlinear Programming Algorithms written by W. I. Zangwill and published by . This book was released on 1968 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conditions which are necessary and sufficient for convergence of a nonlinear programming algorithm are stated. It is also shown that the convergence conditions can be easily applied to most programming algorithms. As examples, algorithms by Arrow, Hurwicz and Uzawa; Cauchy; Frank and Wolfe; and Newton-Raphson are proven to converge by direct application of the convergence conditions. Also the Topkis-Veinott convergence conditions for feasible direction algorithms are shown to be a special case of the conditions stated in this paper. (Author).
Download or read book Encyclopedia of Optimization written by Christodoulos A. Floudas and published by Springer Science & Business Media. This book was released on 2008-09-04 with total page 4646 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".
Download or read book Computer Sciences Technical Report written by and published by . This book was released on 1993 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonlinear Programming 2 written by Olvi L. Mangasarian and published by . This book was released on 1975 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Convergence properties of a class of minimization algorithms; Convergence of the reduced gradient method; A quasi-newton method for unconstrained minimization problems; Superlinearly convergent algorithms for linearly constrained optimization; An ideal penalty function for constrained optimization; On penalty and multiplier methods for constrained minimization; Rate of convergence of the method of multipliers with inexact minimization; Optimization with corners; The use of matrix factorizations in derivative-free nonlinear least squares algorithms; Newton derived methods for nonlinear equations and inequalities; Disjunctive programming: cutting planes from logical conditions.
Download or read book Technical Reports Awareness Circular TRAC written by and published by . This book was released on 1988-07 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Second Order Variational Analysis in Optimization Variational Stability and Control written by Boris S. Mordukhovich and published by Springer Nature. This book was released on with total page 802 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Superlinearly Globally Convergent Algorithms for Nonlinear Programming Via Sequential Linear Programs written by Jerome Lawrence Kreuser and published by . This book was released on 1979 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Variational Trajectory Optimization Tool Set written by Robert R. Bless and published by . This book was released on 1993 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book International Conference on Intelligent Computing Intelligent computing written by De-Shuang Huang and published by Springer Science & Business Media. This book was released on 2006-08-04 with total page 1357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the International Conference on Intelligent Computing, ICIC 2006, held in Kunming, China, August 2006. The book collects 161 carefully chosen and revised full papers. Topical sections include neural networks, evolutionary computing and genetic algorithms, kernel methods, combinatorial and numerical optimization, multiobjective evolutionary algorithms, neural optimization and dynamic programming, as well as case-based reasoning and probabilistic reasoning.
