A note on kkt-invexity in nonsmooth continuous-time optimization
DOI:
https://doi.org/10.4067/S0716-09172007000300005Keywords:
Nonsmooth continuous-time optimization, KKT conditions, KKT-invexity.Abstract
We introduce the notion of KKT-invexity for nonsmooth continuoustime nonlinear optimization problems and prove that this notion is a necessary and sufficient condition for every KKT solution to be a global optimal solution.
References
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[7] M. A. Rojas-Medar, A.J.V. Brand˜ao and G.N. Silva, Nonsmooth continuous-time optimization problems: sufficient conditions, J. Math. Anal.Appl., 227, pp. 305-318, (1998).
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[2] A. J. V. Brand˜ao, M. A. Rojas-Medar and G.N. Silva, Nonsmooth continuous-time optimization problems: necessary conditions, Comp. Math. with Appl., 41, pp. 1477-1486, (2001).
[3] F. H. Clarke, Optimization and nonsmooth analysis, Classics in Applied Mathematics 5, SIAM, (1990).
[4] M. A. Hanson, On sufficiency of Kuhn-Tucker conditions, J. Math. Anal. Appl., 30, pp. 545-550, (1981).
[5] D. H. Martin, The essence of invexity, J. Optim. Theory Appl., 47, pp. 65-76, (1985).
[6] V. A. de Oliveira and M.A. Rojas-Medar, Continuous-time optimization problems involving invex functions, J. Math. Anal. Appl., 327, pp. 1320-1334, (2007).
[7] M. A. Rojas-Medar, A.J.V. Brand˜ao and G.N. Silva, Nonsmooth continuous-time optimization problems: sufficient conditions, J. Math. Anal.Appl., 227, pp. 305-318, (1998).
[8] G. J. Zalmai, A continuous-time generalization of Gordan’s transposition theorem, J. Math. Anal. Appl., 110, pp. 130-140, (1985).
[9] G. J. Zalmai, The Fritz John and Kuhn-Tucker optimality conditions in continuous-time nonlinear programming, J. Math. Anal. Appl., 110, pp. 503-518, (1985).
Published
2017-04-12
How to Cite
[1]
V. Antunes de Oliveira, M. A. Rojas Medar, and Vieira Brandão A. J., “A note on kkt-invexity in nonsmooth continuous-time optimization”, Proyecciones (Antofagasta, On line), vol. 26, no. 3, pp. 269-279, Apr. 2017.
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