Journal of Optimization Theory and Applications

, Volume 155, Issue 1, pp 145–164

# Exact Penalty and Optimality Condition for Nonseparable Continuous Piecewise Linear Programming

Article

## 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

## Notes

### Acknowledgements

This research was supported jointly by the National Natural Science Foundation of China (61074118, 60974008, 61104218, 041306020) and the Research Fund of Doctoral Program of Higher Education (200800030029).

The authors appreciate the reviewers for their insightful comments and helpful suggestions.

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