Related papers: Strong valid inequalities for a class of concave s…

We consider robust submodular maximization problems (RSMs), where given a set of $m$ monotone submodular objective functions, the robustness is with respect to the worst-case (scaled) objective function. The model we consider generalizes…

The problem of scheduling conflicting jobs on parallel machines consists in assigning a set of jobs to a set of machines so that no two conflicting jobs are allocated to the same machine, and the maximum processing time among all machines…

Implicit variables of an optimization problem are used to model variationally challenging feasibility conditions in a tractable way while not entering the objective function. Hence, it is a standard approach to treat implicit variables as…

We consider the nonconvex set $\mathcal S_n = \{(x,X,z): X = x x^T, \; x (1-z) =0,\; x \geq 0,\; z \in \{0,1\}^n\}$, which is closely related to the feasible region of several difficult nonconvex optimization problems such as the best…

In this note we explore duality in reverse convex optimization with reverse convex inequality constraints. While we are examining the special case of a finite index set of the inequality constraints, we are primarily interested in the…

This paper studies simple bilevel problems, where a convex upper-level function is minimized over the optimal solutions of a convex lower-level problem. We first show the fundamental difficulty of simple bilevel problems, that the…

In the framework of a real Hilbert space we consider the problem of approaching solutions to a class of hierarchical variational inequality problems, subsuming several other problem classes including certain mathematical programs under…

We define two non-linear operations with random (not necessarily closed) sets in Banach space: the conditional core and the conditional convex hull. While the first is sublinear, the second one is superlinear (in the reverse set inclusion…

Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…

Many practical optimization problems lack strong convexity. Fortunately, recent studies have revealed that first-order algorithms also enjoy linear convergences under various weaker regularity conditions. While the relationship among…

Submodular set-functions have many applications in combinatorial optimization, as they can be minimized and approximately maximized in polynomial time. A key element in many of the algorithms and analyses is the possibility of extending the…

We consider polyhedral approximations of strictly convex compacta in finite dimensional Euclidean spaces (such compacta are also uniformly convex). We obtain the best possible estimates for errors of considered approximations in the…

Computing mixed volume of convex polytopes is an important problem in computational algebraic geometry. This paper establishes sufficient conditions under which the mixed volume of several convex polytopes exactly equals the normalized…

This paper presents a convex sufficient condition for solving a system of nonlinear equations under parametric changes and proposes a sequential convex optimization method for solving robust optimization problems with nonlinear equality…

It is important to design separation algorithms of low computational complexity in mixed integer programming. We study the separation problems of the two continuous knapsack polyhedra with divisible capacities. The two polyhedra are the…

Motivated by robust matrix recovery problems such as Robust Principal Component Analysis, we consider a general optimization problem of minimizing a smooth and strongly convex loss function applied to the sum of two blocks of variables,…

Bilevel programs model sequential decision interactions between two sets of players and find wide applications in real-world complex systems. In this paper, we consider a bilevel mixed-integer linear program with binary tender, wherein the…

Multiclass problems are often decomposed into multiple binary problems that are solved by individual binary classifiers whose results are integrated into a final answer. Various methods, including all-pairs (APs), one-versus-all (OVA), and…

A variational principle is introduced to provide a new formulation and resolution for several boundary value problems with a variational structure. This principle allows one to deal with problems well beyond the weakly compact structure. As…

We consider joint optimization and learning problems arising in real-time decision systems. While most existing work focuses primarily on convex, revenue-based objectives, we extend this line of research to multi-objective formulations. In…