The constraint qualification for dc programming problems with convex set constraints
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Abstract
In this paper, we provide a necessary and sufficient constraint qualification for optimal conditions in DC programming problems with constraints of convex inequality systems and a convex set. We also set up necessary and sufficient qualifications for optimal conditions in fractional and weakly convex programming problems with constraints of convex inequality systems and a convex set.
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References
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[10]. M. V. Ramana, L. Tucel, and H. Wolewicz (1997), “Strong duality for semi-definite grogramming”, SIAMJ. Optim., (7), pp. 644-662.
[2]. L. T. H. An and P. D. Tao (2005), “The DC (difference of convex functions) programming and DCA revisited with DC models of real world non-convex optimization problems”, Ann. Oper. Res., (133), pp. 23-46.
[3]. H. Bauschke, J. Borwein, and W. Li (1999), “Strong conical hull intersection property, bounded linear regularity, Jameson’s property (G), and error bounds in convex optimization”, Math.
Program., (86), pp. 135-160.
[4]. H. H. Bauschke, J. M. Borwein, and W. Li (2002), “Nonlinearly constrained best approximation in Hilbert space: The strong chip and the basic constraint qualification”, SIAM J. Optim., (13), pp. 228-239.
[5]. J. B. Hiriart-Urruty and C. Lemaréchal (1993), Convex analysis and minimization algorithmsi, Springer-Verlag, Berlin, Heidelberg, Germany.
[6]. C. Li, K. F. Ng, and T. K. Pong (2008), “Constraint qualifications for convex inequality systems with applications in constrained optimization”, SIAM J. Optim., (19), pp. 163-187.
[7]. V. Jeyakumar, A. Rubinov, B.M. Glover, and Y. Ishizuka (1996), “Inequality systems and global optimization”, J. Math. Anal. Appl., (202), pp. 900-919.
[8]. J. Peypouquet, Convex optimization in normed spaces: Theory, methods and examples (2015), Springer, Cham.
[9]. Y. Saeki, S. Suzuki and D. Kuroiwa (2011), “A necessary and sufficient constraint qualification for DC programming problems with convex inequality constraints”, Scientiae Mathematicae Japonicae, pp. 169-174.
[10]. M. V. Ramana, L. Tucel, and H. Wolewicz (1997), “Strong duality for semi-definite grogramming”, SIAMJ. Optim., (7), pp. 644-662.
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