On Optimality Conditions For Singular Constrained Optimization
Download On Optimality Conditions For Singular Constrained Optimization PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get On Optimality Conditions For Singular Constrained Optimization book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages.
On Optimality Conditions for Singular Constrained Optimization
Abstract: "Optimality conditions for singular constrained optimization are not well understood. When the constrained gradient matrix is rank deficient at the solution, the Kuhn-Tucker conditions may not be satisfied. This paper introduces and discusses several optimality conditions for singular constrained optimization problems for the case when the constraint gradient matrix at the solution is rank deficient. These conditions are a generalization of the traditional Kuhn-Tucker conditions for constrained optimization. A class of 'nice' singular constrained problems is identified and is shown to satisfy these conditions. We also give examples of singular constrained problems that do not satisfy these conditions, and point out fundamental differences between these problems and the nice problems. These conditions have useful implications both for constructing algorithms and for analyzing methods for singular constrained optimization problems."
Real-time PDE-constrained Optimization
Many engineering and scientific problems in design, control, and parameter estimation can be formulated as optimization problems that are governed by partial differential equations (PDEs). The complexities of the PDEs--and the requirement for rapid solution--pose significant difficulties. A particularly challenging class of PDE-constrained optimization problems is characterized by the need for real-time solution, i.e., in time scales that are sufficiently rapid to support simulation-based decision making. Real-Time PDE-Constrained Optimization, the first book devoted to real-time optimization for systems governed by PDEs, focuses on new formulations, methods, and algorithms needed to facilitate real-time, PDE-constrained optimization. In addition to presenting state-of-the-art algorithms and formulations, the text illustrates these algorithms with a diverse set of applications that includes problems in the areas of aerodynamics, biology, fluid dynamics, medicine, chemical processes, homeland security, and structural dynamics. Audience: readers who have expertise in simulation and are interested in incorporating optimization into their simulations, who have expertise in numerical optimization and are interested in adapting optimization methods to the class of infinite-dimensional simulation problems, or who have worked in "offline" optimization contexts and are interested in moving to "online" optimization.
Convex Optimization
Author: Stephen P. Boyd
language: en
Publisher: Cambridge University Press
Release Date: 2004-03-08
Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.