Sequentially necessary and sufficient conditions for solutions of optimization problems with inclusion constraints
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Abstract
In this paper, we provide sequentially necessary and sufficient conditions for optimal solutions of optimization problems with inclusion constraints. The sequentially optimal conditions obtained are without any constraints.
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Keywords
Sequence, solutions of optimization problem, inclusion constraint
References
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[10]. L. Thibault (1997), “Sequential convex subdifferential calculus and Lagrange multipliers”, Siam J. Control Optim., (7), p. 641-662.
[2]. A. Brondsted and R. T. Rockafellar (1965), “On the subdifferentiability of convex functions”, Proc. Amer. Math. Soc., (16), p. 605-611.
[3]. S. Dempe and A. B. Zemkoho (2012), “On the Karush-Kuhn-Tucker reformulation of the bilevel optimization problem”, Nonlinear Anal., (75), p. 1202-1218.
[4]. S. Dempe, N. Dinh, and J. Dutta (2010), “Optimality Conditions for a Simple Convex Bilevel Programming Problem”, Variational Analysis and Generalized Differentiation in Optimization and Control Springer Optimization and Its Applications, (47), p. 149-161.
[5]. A. Dhara and J. Dutta (2012), Optimality Conditions in Convex Optimization, A Finite-Dimension View, Taylor and Francis Group.
[6]. W. Heins and S. K. Mitter (1970), “Conjugate convex function, Duality and Optimal control, Problem I: Systems Governed Ordinary Differential equations”, Inform. Sciences, (2), p. 211-243.
[7]. V. Jeyakumar, G. M. Lee, and N. Dinh (2003), “New sequential Lagrange multiplier conditions charactering optimality without constraint qualification for convex programs”, Siam J. Optim., (14), p. 534-547.
[8]. V. Jeyakumar, A. M. Rubinov, B. M. Glover, and Y. Ishizuka (1996), “Inequality systems and Global optimization”, J. Math. Anal. App., (202), p. 900-919.
[9]. P. Kanniappan (1983), “ Necessary condition for optimality of nondifferentiable convex multiobjective programming”, J. Optim. Theory and App., (40), p. 167-174.
[10]. L. Thibault (1997), “Sequential convex subdifferential calculus and Lagrange multipliers”, Siam J. Control Optim., (7), p. 641-662.
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