In this paper we consider a semi-infinite relaxation of mixed integer linear programs. We show that minimal valid inequalities for this relaxation correspond to maximal latticefree convex sets, and that they arise from nonnegative, piecewise linear, positively homogeneous, convex functions.

The Kantorovich function (xT Ax)(xT A−1x), where A is a positive definite matrix, is not convex in general. From a matrix or convex analysis point of view, it is interesting to address the question: When is this function convex? In this paper, we prove that the 2dimensional Kantorovich function is convex if and only if the condition number of its matrix is less than or equal to 3 + 2 √ 2. Thus ...

In this paper, we introduce and study a class of generalized symmetric vector quasi-equilibrium problems in abstract convex spaces. By virtue of the properties of Γ-convex and KC-map, we give some sufficient conditions to guarantee the existence of solutions for the generalized symmetric vector quasi-equilibrium problems in abstract convex spaces. As application, we show an existence theorem of...

In this paper, convex continuous-time programming problem with inequality type of constraints is considered. We derive new saddle point optimality conditions and classical duality results such as weak strong properties, under additional regularity assumption. A fundamental tool, employed in the derivation necessary criteria result for programming, a version theorem alternative infinite-dimensio...

We consider a nonsmooth semi-infinite interval-valued vector programming problem, where the objectives and constraint functions need not to be locally Lipschitz. Using Abadie’s qualification convexificators, we provide Karush–Kuhn–Tucker necessary optimality conditions by converting initial problem into bi-criteria optimization problem. Furthermore, establish sufficient under asymptotic convexi...

As a first-order method, the augmented Lagrangian method (ALM) is a benchmark solver for linearly constrained convex programming, and in practice some semi-definite proximal terms are often added to its primal variable's subproblem to make it more implementable. In this paper, we propose an accelerated PALM with indefinite proximal regularization (PALM-IPR) for convex programming with linear co...

We study stochastic linear programming games: a class of stochastic cooperative games whose payoffs under any realization of uncertainty are determined by a specially structured linear program. These games can model a variety of settings, including inventory centralization and cooperative network fortification. We focus on the core of these games under an allocation scheme that determines how p...

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.

This article is concerned with the set-membership state estimation problem for power distribution networks (PDNs) over a resource-constrained communication network under influence of unknown but bounded (UBB) noises. Firstly, in order to alleviate pressure information (ICN) while meeting requirements, event-triggered mechanism adopted send data containing more valid center, reasonably reducing ...