Optimality conditions in convex optimization with locally Lipschitz constraints
Tóm tắt
In this paper, we consider a convex optimization problem with locally Lipschitz inequality constraints. The KKT optimality conditions (both necessary and sufficient) for quasi
$$\epsilon $$
-solutions are established under Slater’s constraint qualification and a non-degeneracy condition. Moreover, we explore the optimality condition for weakly efficient solutions in multiobjective convex optimization involving locally Lipschitz constraints. Some examples are given to illustrate our results.
Tài liệu tham khảo
Clarke, F.H.: Optimization and Nonsmooth Analysis. Classics in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (1990)
Dhara, A., Dutta, J.: Optimality Conditions in Convex Optimization: A Finite-Dimensional View. CRC Press, Cambridge (2012)
Dutta, J., Lalitha, C.S.: Optimality conditions in convex optimization revisited. Optim. Lett. 7, 221–229 (2013)
Ehrgott, M.: Multicriteria Optimization, 2nd edn. Springer, Berlin (2005)
Ekeland, I.: On the variational principle. J. Math. Anal. Appl. 47, 324–353 (1974)
Jiao, L.G., Lee, J.H.: Approximate optimality and approximate duality for quasi approximate solutions in robust convex semidefinite programs. J. Optim. Theory Appl. 176, 74–93 (2018)
Lasserre, J.B.: On representations of the feasible set in convex optimization. Optim. Lett. 4, 1–5 (2010)
Lee, J.H., Jiao, L.G.: On quasi \(\epsilon \)-solution for robust convex optimization problems. Optim. Lett. 11, 1609–1622 (2017)
Loridan, P.: Necessary conditions for \(\epsilon \)-optimality. Math. Program. Stud. 19, 140–152 (1982)
Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Springer, Berlin (2001)
Yamamoto, S., Kuroiwa, D.: Constraint qualifications for KKT optimality condition in convex optimization with locally Lipschitz inequalty constraints. Linear Nonlinear Anal. 2, 101–111 (2016)