Exact Penalty and Optimality Condition for Nonseparable Continuous Piecewise Linear Programming

Xiaolin Huang (), Jun Xu () and Shuning Wang ()
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Xiaolin Huang: Tsinghua University
Jun Xu: Tsinghua University
Shuning Wang: Tsinghua University

Journal of Optimization Theory and Applications, 2012, vol. 155, issue 1, No 7, 145-164

Abstract: 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.

Keywords: Piecewise linear; Nonlinear programming; Exact penalty; Local optimality condition (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10957-012-0032-7

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