Related papers: The constant objective value property for combinat…
This paper is devoted to variational problems on the set of probability measures which involve optimal transport between unequal dimensional spaces. In particular, we study the minimization of a functional consisting of the sum of a term…
This article discusses some difficulties in the implementation of combinatorial algorithms associated with the choice of all elements with certain properties among the elements of a set with great cardinality.The problem has been resolved…
Multi-modal multi-objective optimization is to locate (almost) equivalent Pareto optimal solutions as many as possible. While decomposition-based evolutionary algorithms have good performance for multi-objective optimization, they are…
We characterize the extreme points of the set of incentive-compatible mechanisms for screening problems with linear utility. Our framework subsumes problems with and without transfers, such as monopoly pricing, principal-optimal bilateral…
We study the assignment problem of objects to agents with heterogeneous preferences under distributional constraints. Each agent is associated with a publicly known type and has a private ordinal ranking over objects. We are interested in…
This paper studies the unification problem with associative, commutative, and associative-commutative functions mainly from a viewpoint of the parameterized complexity on the number of variables. It is shown that both associative and…
Multi-objective unconstrained combinatorial optimization problems (MUCO) are in general hard to solve, i.e., the corresponding decision problem is NP-hard and the outcome set is intractable. In this paper we explore special cases of MUCO…
We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…
This article investigates a distributed aggregative optimization problem subject to coupled affine inequality constraints, in which local objective functions depend not only on their own decision variables but also on an aggregation of all…
Bayesian Optimization (BO) has shown significant success in tackling expensive low-dimensional black-box optimization problems. Many optimization problems of interest are high-dimensional, and scaling BO to such settings remains an…
Given a strictly convex multiobjective optimization problem with objective functions $f_1,\dots,f_N$, let us denote by $x_0$ its solution, obtained as minimum point of the linear scalarized problem, where the objective function is the…
In this paper, we study possible extensions of the main ideas and methods of constrained DC optimization to the case of nonlinear semidefinite programming problems and more general nonlinear and nonsmooth cone constrained optimization…
We consider the problem of minimizing the continuous valued total variation subject to different unary terms on trees and propose fast direct algorithms based on dynamic programming to solve these problems. We treat both the convex and the…
We show global uniqueness of the solution to a class of constrained variational problems, using scaling properties. This is used to establish the essential uniqueness of solutions of a large deviations problem in multiple dimensions. The…
We propose an algorithm for a family of optimization problems where the objective can be decomposed as a sum of functions with monotonicity properties. The motivating problem is optimization of hyperparameters of machine learning…
Combinatorial optimization problems are ubiquitous in industry. In addition to finding a solution with minimum cost, problems of high relevance involve a number of constraints that the solution must satisfy. Variational quantum algorithms…
In the $k$-Orthogonal Vectors ($k$-OV) problem we are given $k$ sets, each containing $n$ binary vectors of dimension $d=n^{o(1)}$, and our goal is to pick one vector from each set so that at each coordinate at least one vector has a zero.…
We propose a novel decomposition framework for the distributed optimization of Difference Convex (DC)-type nonseparable sum-utility functions subject to coupling convex constraints. A major contribution of the paper is to develop for the…
The idea behind object-centric representation learning is that natural scenes can better be modeled as compositions of objects and their relations as opposed to distributed representations. This inductive bias can be injected into neural…
Transportation networks are inevitably selected with reference to their global cost which depends on the strengths and the distribution of the embedded currents. We prove that optimal current distributions for a uniformly injected…