In this paper, we propose a new stochastic gradient method for numerical minimization of finite sums. We also propose a modified version of this method applicable on more general problems referred to as infinite sum problems, where the objective function is in the form of mathematical expectation. The method is based on a strategy to … Read more
Over the past two decades, descent methods have received substantial attention within the multiobjective optimization field. Nonetheless, both theoretical analyses and empirical evidence reveal that existing first-order methods for multiobjective optimization converge slowly, even for well-conditioned problems, due to the objective imbalances. To address this limitation, we incorporate curvature information to scale each objective within … Read more
We consider a two-player Nash game in which each player represents a fleet of unmanned aerial vehicles. Each fleet is supposed to distribute information among fleet members, while simultaneously trying to prevent the opposite fleet from achieving this. Using the electro-magnetic spectrum’s properties, we model each fleet’s task as a nonlinear Nash game. By reformulating … Read more
We present an optimization algorithm that can identify a global minimum of a potentially nonconvex smooth function with high probability, assuming the Gibbs measure of the potential satisfies a logarithmic Sobolev inequality. Our contribution is twofold: on the one hand we propose a global optimization method, which is built on an oracle sampling algorithm producing … Read more
This paper studies the problems of partitioning the vertices of a graph G = (V,E) into (or covering with) a minimum number of low-diameter clusters from the lenses of approximation algorithms and integer programming. Here, the low-diameter criterion is formalized by an s-club, which is a subset of vertices whose induced subgraph has diameter at … Read more
Given a Hilbert space and a finite family of operators defined on the space, the common fixed point problem (CFPP) is the problem of finding a point in the intersection of the fixed point sets of these operators. A particular case of the problem, when the operators are orthogonal projections, is the convex feasibility problem … Read more
This paper systematically surveys useful properties of the epigraph reformulation for optimization problems, and complements them by some new results. We focus on the complete compatibility of the original formulation and the epigraph reformulation with respect to solvability and unsolvability, the compatibility with respect to some, but not all, basic constraint qualifications, the formulation of … Read more
For almost two decades, mixed integer programming (MIP) solvers have used graph- based conflict analysis to learn from local infeasibilities during branch-and-bound search. In this paper, we improve MIP conflict analysis by instead using reasoning based on cuts, inspired by the development of conflict-driven solvers for pseudo- Boolean optimization. Phrased in MIP terminology, this type … Read more
For equality-constrained linear mixed-integer programs (MIP) defined by rational data, it is known that the subadditive dual is a strong dual and that there exists an optimal solution of a particular form, termed generator subadditive function. Motivated by these results, we explore the connection between Lagrangian duality, subadditive duality and generator subadditive functions for general … Read more
This paper develops a parameter-free adaptive proximal bundle method with two important features: 1) adaptive choice of variable prox stepsizes that “closely fits” the instance under consideration; and 2) adaptive criterion for making the occurrence of serious steps easier. Computational experiments show that our method performs substantially fewer consecutive null steps (i.e., a shorter cycle) … Read more