We propose an approach to find the optimal value of a convex semi-infinite program (SIP) that involves identifying finite set relevant constraints by solving finite-dimensional global maximization problem. One major advantages our is it admits plug-and-play module where any suitable optimization algorithm can be employed obtain SIP. As example, we simulated annealing based which useful especial...

This paper provides KKT and saddle point optimality conditions, duality theorems and stability theorems for consistent convex optimization problems posed in locally convex topological vector spaces. The feasible sets of these optimization problems are formed by those elements of a given closed convex set which satisfy a (possibly in…nite) convex system. Moreover, all the involved functions are ...

This paper concerns a closedness condition called (CC), requiring a convex function and a convex constrained system. This type of condition has played an important role in the study of convex optimization problems. Our aim is to establish several characterizations of this condition and to apply them to study minimizing problems involving a DC function under a cone-convex constraint and a set co...

In this paper, we study the problem of learning from weakly labeled data, where labels of the training examples are incomplete. This includes, for example, (i) semi-supervised learning where labels are partially known; (ii) multi-instance learning where labels are implicitly known; and (iii) clustering where labels are completely unknown. Unlike supervised learning, learning with weak labels in...

We study the convex hull of the feasible set of the semi-continuous knapsack problem, in which the variables belong to the union of two intervals. Besides being important in its own right, the semi-continuous knapsack problem is a relaxation of general mixed-integer programming. We show how strong inequalities valid for the semi-continuous knapsack polyhedron can be derived and used in a branch...

This paper deals with the characterization of the sums of compact convex sets with linear subspaces, simplices, sandwiches (convex hulls of pairs of parallel affine manifolds) and parallelotopes in terms of the so-called internal and conical representations, topological and geometrical properties. In particular, it is shown that a closed convex set is a sandwich if and only if its relative boun...

We study a specific convex maximization problem in the space of continuous functions defined on a semi-infinite interval. An unexplained connection to the discrete version of this problem is investigated.

In this paper, we characterize lower semi-continuous pseudo-convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ with respect to the pseudo-monotonicity its Clarke-Rockafellar Sub-differential. We extend results characterizations non-smooth monotonicity sub-differentials spaces.