Exact Penalty and Optimality Condition for Nonseparable Continuous Piecewise Linear Programming

Exact Penalty and Optimality Condition for Nonseparable Continuous Piecewise Linear Programming

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Article ID: iaor20126119
Volume: 155
Issue: 1
Start Page Number: 145
End Page Number: 164
Publication Date: Oct 2012
Journal: Journal of Optimization Theory and Applications
Authors: , ,
Keywords: programming: linear
Abstract:

Utilizing compact representations for continuous piecewise linear functions, this paper discusses some theoretical properties for nonseparable continuous piecewise linear programming. The existence of exact penalty for continuous piecewise linear programming is proved, which allows us to concentrate on unconstrained problems. For unconstrained problems, we give a sufficient and necessary local optimality condition, which is based on a model with universal representation capability and hence applicable to arbitrary continuous piecewise linear programming. From the gained optimality condition, an algorithm is proposed and evaluated by numerical experiments, where the theoretical properties are illustrated as well.

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