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Global optimality conditions and exact penalization

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Abstract

This paper addresses the nonconvex optimization problem with the cost function and the inequality constraints given by d.c. functions. The original problem is reduced to a problem without inequality constraints by means of the exact penalization techniques. Furthermore, the penalized problem is presented as a d.c. minimization problem. For the latter problem we develop the global optimality conditions (GOCs) which reduce the nonconvex optimization problem to a family of convex (linearized with respect to the basic nonconvexity) problems. In addition,the GOCs are related to the KKT theorem for the original problem. Besides, the GOCs possess the so-called constructive (algorithmic) property which, if the GOCs are violated, implies the construction of a feasible point that is better (in the sense of the original problem) than the one in question. The effectiveness of the GOCs is demonstrated by examples.

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Acknowledgements

This research was supported by the Russian Science Foundation (Project No. 15-11-20015).

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  1. Matrosov Institute for System Dynamics & Control Theory SB RAS, Lermontov st., 134, Irkutsk, Russia, 664033

    Alexander S. Strekalovsky

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  1. Alexander S. Strekalovsky
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Correspondence to Alexander S. Strekalovsky.

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Strekalovsky, A.S. Global optimality conditions and exact penalization. Optim Lett 13, 597–615 (2019). https://doi.org/10.1007/s11590-017-1214-x

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  • DOI: https://doi.org/10.1007/s11590-017-1214-x

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