Circular programming problems are a new class of convex optimization problems that include second-order cone programming problems as a special case. Alizadeh and Goldfarb [Math. Program. Ser. A 95 (2003) 3-51] introduced primal-dual path-following algorithms for solving second-order cone programming problems. In this paper, we generalize their work by using the machinery of Euclidean Jordan alg...

For a non-Archimedean locally convex space (E, τ), the finest locally convex topology having the same as τ convergent sequences and the finest locally convex topology having the same as τ compactoid sets are studied.

In this paper some concepts of convex analysis are extended in an intrinsic way from the Euclidean space to the sphere. In particular, relations between convex sets in the sphere and pointed convex cones are presented. Several characterizations of the usual projection onto a Euclidean convex set are extended to the sphere and an extension of Moreau’s theorem for projection onto a pointed convex...

This is a review paper on some new inequalities for convex functions of one and several variables. The most important result presented for convex functions of one variable is the extension of Jensen’s inequality to affine combinations. The most interesting results presented for convex functions of several variables refer to inequalities concerning simplexes and its cones. Mathematics subject cl...

The BCQ and the Abadie CQ for infinite systems of convex inequalities in Banach spaces are characterized in terms of the upper semi-continuity of the convex cones generated by the subdifferentials of active convex functions. Some relationships with other constraint qualifications such as the CPLV and the Slate condition are also studied. Applications in best approximation theory are provided.

We introduce a new class of cooperative games by using the notion of local supermodularity. Therefore locally convex games can be considered as relaxations of convex games. Moreover, we obtain a characterization of a subclass of locally concave games in terms of the rank function of a matroid.

We introduce a new class of cooperative games by using the notion of local supermodularity. Therefore locally convex games can be considered as relaxations of convex games. Cooperative games with the unit marginal worth property are defined and characterizations of locally concave (convex) games with this property are proved. Moreover, we obtain a characterization of a subclass of locally conca...