<inline-formula> <graphic file="1687-1812-2011-175327-i1.gif"/></inline-formula>-Optimal Solutions in Nonconvex Semi-Infinite Programs with Support Functions

• Main Authors: Son TaQuang, Kim DoSang
• Format: Article
• Language: English
• Published: SpringerOpen 2011-01-01
• Series: Fixed Point Theory and Applications
• Online Access: http://www.fixedpointtheoryandapplications.com/content/2011/175327

<p>Abstract</p> <p>Approximate optimality conditions for a class of nonconvex semi-infinite programs involving support functions are given. The objective function and the constraint functions are locally Lipschitz functions on <inline-formula> <graphic file="1687-1812-2011-175327-i2.gif"/></inline-formula>. By using a Karush-Kuhn-Tucker (KKT) condition, we deduce a necessary optimality condition for local approximate solutions. Then, generalized KKT conditions for the problems are proposed. Based on properties of <inline-formula> <graphic file="1687-1812-2011-175327-i3.gif"/></inline-formula>-semiconvexity and semiconvexity applied to locally Lipschitz functions and generalized KKT conditions, we establish sufficient optimality conditions for another kind of local approximate solutions of the problems. Obtained results in case of nonconvex semi-infinite programs and nonconvex infinite programs are discussed.</p>