Related papers: Inapproximability of Combinatorial Optimization Pr…
Comparing, or benchmarking, of optimization algorithms is a complicated task that involves many subtle considerations to yield a fair and unbiased evaluation. In this paper, we systematically review the benchmarking process of optimization…
We discuss the notion of optimal polynomial approximants in multivariable reproducing kernel Hilbert spaces. In particular, we analyze difficulties that arise in the multivariable case which are not present in one variable, for example, a…
Neural Combinatorial Optimization approaches have recently leveraged the expressiveness and flexibility of deep neural networks to learn efficient heuristics for hard Combinatorial Optimization (CO) problems. However, most of the current…
We consider stochastic settings for clustering, and develop provably-good approximation algorithms for a number of these notions. These algorithms yield better approximation ratios compared to the usual deterministic clustering setting.…
There exist combable groups in which the conjugacy problem is unsolvable. The isomorphism problem is unsolvable for certain recursive sequences of finite presentations of combable groups.
Methods for the reduction of the complexity of computational problems are presented, as well as their connections to renormalization, scaling, and irreversible statistical mechanics. Several statistically stationary cases are analyzed; for…
The primary focus of this paper is on designing an inexact first-order algorithm for solving constrained nonlinear optimization problems. By controlling the inexactness of the subproblem solution, we can significantly reduce the…
We investigate finite-dimensional constrained structured optimization problems, featuring composite objective functions and set-membership constraints. Offering an expressive yet simple language, this problem class provides a modeling…
We show improved NP-hardness of approximating Ordering Constraint Satisfaction Problems (OCSPs). For the two most well-studied OCSPs, Maximum Acyclic Subgraph and Maximum Betweenness, we prove inapproximability of $14/15+\epsilon$ and…
We determine the power of the weighted sum scalarization with respect to the computation of approximations for general multiobjective minimization and maximization problems. Additionally, we introduce a new multi-factor notion of…
We consider list versions of sparse approximation problems, where unlike the existing results in sparse approximation that consider situations with unique solutions, we are interested in multiple solutions. We introduce these problems and…
In the regime of bounded transportation costs, additive approximations for the optimal transport problem are reduced (rather simply) to relative approximations for positive linear programs, resulting in faster additive approximation…
Combinatorial optimization problems pose significant computational challenges across various fields, from logistics to cryptography. Traditional computational methods often struggle with their exponential complexity, motivating exploration…
We introduce an algorithm design technique for a class of combinatorial optimization problems with concave costs. This technique yields a strongly polynomial primal-dual algorithm for a concave cost problem whenever such an algorithm exists…
Submodular functions and their optimization have found applications in diverse settings ranging from machine learning and data mining to game theory and economics. In this work, we consider the constrained maximization of a submodular…
A rational approximation by a ratio of polynomial functions is a flexible alternative to polynomial approximation. In particular, rational functions exhibit accurate estimations to nonsmooth and non- Lipschitz functions, where polynomial…
We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic…
We analyze combinatorial optimization problems with ordinal, i.e., non-additive, objective functions that assign categories (like good, medium and bad) rather than cost coefficients to the elements of feasible solutions. We review different…
We consider problems of rating alternatives based on their pairwise comparison under various assumptions, including constraints on the final scores of alternatives. The problems are formulated in the framework of tropical mathematics to…
Numerically computing global policies to optimal control problems for complex dynamical systems is mostly intractable. In consequence, a number of approximation methods have been developed. However, none of the current methods can quantify…