相关论文: Approximation algorithms for the vertex happiness

This paper considers stochastic convex optimization problems with smooth functional constraints arising in constrained estimation and robust signal recovery. We operate in the high-dimensional and highly-constrained setting, where oracle…

We consider the task of fitting low-dimensional embeddings to high-dimensional data. In particular, we study the $k$-Euclidean Metric Violation problem ($\textsf{$k$-EMV}$), where the input is $D \in \mathbb{R}^{\binom{n}{2}}_{\geq 0}$ and…

Submodular maximization generalizes many fundamental problems in discrete optimization, including Max-Cut in directed/undirected graphs, maximum coverage, maximum facility location and marketing over social networks. In this paper we…

This paper presents a novel outer approximation algorithm for nonsmooth mixed-integer nonlinear programming (MINLP) problems. The method proceeds by fixing the integer variables and solving the resulting nonlinear convex subproblem. When…

We consider a natural generalization of the Partial Vertex Cover problem. Here an instance consists of a graph G = (V,E), a positive cost function c: V-> Z^{+}, a partition $P_1,..., P_r$ of the edge set $E$, and a parameter $k_i$ for each…

One of the most important open problems in machine scheduling is the problem of scheduling a set of jobs on unrelated machines to minimize the makespan. The best known approximation algorithm for this problem guarantees an approximation…

Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function. These upper bounds are tight at the current estimate, and each iteration monotonically drives the objective…

Submodular functions have many applications. Matchings have many applications. The bitext word alignment problem can be modeled as the problem of maximizing a nonnegative, monotone, submodular function constrained to matchings in a complete…

This paper is devoted to a new modification of a recently proposed adaptive stochastic mirror descent algorithm for constrained convex optimization problems in the case of several convex functional constraints. Algorithms, standard and its…

This paper develops new semidefinite programming (SDP) relaxation techniques for two classes of mixed binary quadratically constrained quadratic programs (MBQCQP) and analyzes their approximation performance. The first class of problem…

We study the problem of sampling an approximately uniformly random satisfying assignment for atomic constraint satisfaction problems i.e. where each constraint is violated by only one assignment to its variables. Let $p$ denote the maximum…

A large number of problems in optimization, machine learning, signal processing can be effectively addressed by suitable semidefinite programming (SDP) relaxations. Unfortunately, generic SDP solvers hardly scale beyond instances with a few…

Given a nonlinear, univariate, bounded, and differentiable function $f(x)$, this article develops a sequence of Mixed Integer Linear Programming (MILP) and Linear Programming (LP) relaxations that converge to the graph of $f(x)$ and its…

This paper proposes two convergent adaptive mesh-refining algorithms for the hybrid high-order method in convex minimization problems with two-sided p-growth. Examples include the p-Laplacian, an optimal design problem in topology…

Based on the ideas of arXiv:1710.06612, we consider the problem of minimization of the Holder-continuous non-smooth functional $f$ with non-positive convex (generally, non-smooth) Lipschitz-continuous functional constraint. We propose some…

Recently there were proposed some innovative convex optimization concepts, namely, relative smoothness [1] and relative strong convexity [2,3]. These approaches have significantly expanded the class of applicability of gradient-type methods…

We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…

We consider a variational convex relaxation of a class of optimal partitioning and multiclass labeling problems, which has recently proven quite successful and can be seen as a continuous analogue of Linear Programming (LP) relaxation…

Semidefinite programming (SDP) provides a powerful relaxation for the maximum cut problem. For a graph with rational weights, the decision problem of whether the SDP relaxation for the maximum cut problem is exact is known to be $NP$-hard;…

We study two mixed robust/average-case submodular partitioning problems that we collectively call Submodular Partitioning. These problems generalize both purely robust instances of the problem (namely max-min submodular fair allocation…