A new exact penalty method for semi-infinite programming problems
MetadataShow full item record
In this paper, we consider a class of nonlinear semi-infinite optimization problems. These problems involve continuous inequality constraints that need to be satisfied at every point in an infinite index set, as well as conventional equality and inequality constraints. By introducing a novel penalty function to penalize constraint violations, we form an approximate optimization problem in which the penalty function is minimized subject to only bound constraints. We then show that this penalty function is exact—that is, when the penalty parameter is sufficiently large, any local solution of the approximate problem can be used to generate a corresponding local solution of the original problem. On this basis, the original problem can be solved as a sequence of approximate nonlinear programming problems. We conclude the paper with some numerical results demonstrating the applicability of our approach to PID control and filter design.
NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Computational and Applied Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Computational and Applied Mathematics, Vol. 261 (2014). DOI: 10.1016/j.cam.2013.11.010
Showing items related by title, author, creator and subject.
Loxton, Ryan Christopher (2010)In this thesis, we develop numerical methods for solving five nonstandard optimal control problems. The main idea of each method is to reformulate the optimal control problem as, or approximate it by, a nonlinear programming ...
Li, Bin (2011)In this thesis, we consider several types of optimal control problems with constraints on the state and control variables. These problems have many engineering applications. Our aim is to develop efficient numerical methods ...
Yu, Changjun (2012)In this thesis, We propose new computational algorithms and methods for solving four classes of constrained optimization and optimal control problems. In Chapter 1, we present a brief review on optimization and ...