Second-Order KKT-Invexity in Continuous-Time Optimization

Autores

  • Valeriano A. de Oliveira

DOI:

https://doi.org/10.5540/03.2022.009.01.0302

Palavras-chave:

Continuous-Time Optimization, Sufficient Optimality Conditions, Second-Order KKT-Invexity

Resumo

In this paper, we adapt to the context of continuous-time optimization a concept of generalized convexity adequate to work with second-order stationary solutions, which are solutions that satisfy second-order necessary optimality conditions. We show that the second-order necessary optimality conditions become sufficient when the problem satisfies such a generalized convexity concept. We also show that, under a certain regularity assumption, this concept is as general as possible, in the sense that if the problem is such that every second-order stationary solution is an optimal solution, then the problem necessarily satisfies the generalized convexity concept.

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Biografia do Autor

Valeriano A. de Oliveira

Universidade Estadual Paulista (Unesp), Instituto de Biociências, Letras e Ciências Exatas, Departamento de Matemática, Câmpus de São José do Rio Preto, SP

Referências

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V. A. de Oliveira. “Condições de Otimalidade e Dualidade em Otimização Não-Linear com Tempo-Contínuo”. Tese de Livre Docência. Universidade Estadual Paulista (Unesp). São José do Rio Preto. 2019.

V. A. de Oliveira and M. A. Rojas-Medar. “Continuous-time multiobjective optimization problems via invexity”. In: Abstr. Appl. Anal. 2007.1 (2007). Art. ID 61296, 11 pp.

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M. A. Rojas-Medar, A. J. V. Brandão, and G. N. Silva. “Nonsmooth continuous-time optimization problems: sufficient conditions”. In: J. Math. Anal. Appl. 227.2 (1998), pp. 305– 318

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Publicado

2022-12-08

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