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New optimality conditions for nonsmooth control problems

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Abstract

This work considers nonsmooth optimal control problems and provides two new sufficient conditions of optimality. The first condition involves the Lagrange multipliers while the second does not. We show that under the first new condition all processes satisfying the Pontryagin Maximum Principle (called MP-processes) are optimal. Conversely, we prove that optimal control problems in which every MP-process is optimal necessarily obey our first optimality condition. The second condition is more natural, but it is only applicable to normal problems and the converse holds just for smooth problems. Nevertheless, it is proved that for the class of normal smooth optimal control problems the two conditions are equivalent. Some examples illustrating the features of these sufficient concepts are presented.

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  1. Departamento de Matemática Aplicada, Instituto de Biociências, Letras e Ciências Exatas, UNESP - Univ Estadual Paulista, Câmpus de São José do Rio Preto, R. Cristóvão Colombo, 2265, Jd. Nazareth, São José do Rio Preto, SP, 15054-000, Brazil

    Valeriano Antunes de Oliveira & Geraldo Nunes Silva

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  1. Valeriano Antunes de Oliveira
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  2. Geraldo Nunes Silva
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Correspondence to Valeriano Antunes de Oliveira.

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de Oliveira, V.A., Silva, G.N. New optimality conditions for nonsmooth control problems. J Glob Optim 57, 1465–1484 (2013). https://doi.org/10.1007/s10898-012-0003-4

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