We investigate some properties related to the generalized Newton method for the Fischer-Burmeister (FB) function over second-order cones, which allows us to reformulate the second-order cone complementarity problem (SOCCP) as a semismooth system of equations. Specifically, we characterize the B-subdifferential of the FB function at a general point and study the condition for every element of th...

In this paper we study necessary optimality conditions for nonsmooth optimization problems with equality, inequality and abstract set constraints. We derive the enhanced Fritz John condition which contains some new information even in the smooth case than the classical enhanced Fritz John condition. From this enhanced Fritz John condition we derive the enhanced Karush-Kuhn-Tucker (KKT) conditio...

Continuing the work of Hiriart-Urruty and Phelps, we discuss (in both locally convex spaces and Banach spaces) the formulas for the conjugates and subdifferentials of the precomposition of a convex function by a continuous linear mapping and the marginal function of a convex function by a continuous linear mapping. We exhibit a certain (incomplete) duality between the operations of precompositi...

 We consider generalized semi-infinite programming problems in which the index set of the inequality constraints depends on the decision vector and all emerging functions are assumed to be convex. Considering a lower level constraint qualification, we derive a formula for estimating the subdifferential of the value function. Finally, we establish the Fritz-John necessary optimality con...

For a nonsmooth multiobjective mathematical programming problem governed by infinitely many constraints‎, ‎we define a new gap function that generalizes the definitions of this concept in other articles‎. ‎Then‎, ‎we characterize the efficient‎, ‎weakly efficient‎, ‎and properly efficient solutions of the problem utilizing this new gap function‎. ‎Our results are based on $(Phi,rho)-$invexity‎,...