Description: Lagrange-type Functions in Constrained Non-Convex Optimization Please note: this item is printed on demand and will take extra time before it can be dispatched to you (up to 20 working days). Author(s): Alexander M. Rubinov, Xiao-qi Yang Format: Paperback Publisher: Springer-Verlag New York Inc., United States Imprint: Springer-Verlag New York Inc. ISBN-13: 9781461348214, 978-1461348214 Synopsis Lagrange and penalty function methods provide a powerful approach, both as a theoretical tool and a computational vehicle, for the study of constrained optimization problems. However, for a nonconvex constrained optimization problem, the classical Lagrange primal-dual method may fail to find a mini mum as a zero duality gap is not always guaranteed. A large penalty parameter is, in general, required for classical quadratic penalty functions in order that minima of penalty problems are a good approximation to those of the original constrained optimization problems. It is well-known that penaity functions with too large parameters cause an obstacle for numerical implementation. Thus the question arises how to generalize classical Lagrange and penalty functions, in order to obtain an appropriate scheme for reducing constrained optimiza tion problems to unconstrained ones that will be suitable for sufficiently broad classes of optimization problems from both the theoretical and computational viewpoints. Some approaches for such a scheme are studied in this book. One of them is as follows: an unconstrained problem is constructed, where the objective function is a convolution of the objective and constraint functions of the original problem. While a linear convolution leads to a classical Lagrange function, different kinds of nonlinear convolutions lead to interesting generalizations. We shall call functions that appear as a convolution of the objective function and the constraint functions, Lagrange-type functions.
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Book Title: Lagrange-type Functions in Constrained Non-Convex Optimization
Subject Area: Data Analysis
Item Height: 235mm
Item Width: 155mm
Author: Alexander M. Rubinov, Xiao-Qi Yang
Publication Name: Lagrange-Type Functions in Constrained Non-Convex Optimization
Format: Paperback
Language: English
Publisher: Springer-Verlag NY Inc.
Subject: Mathematics, Management
Publication Year: 2013
Type: Textbook
Item Weight: 468g
Number of Pages: 286 Pages
