Related papers: On Constrained Mixed-Integer DR-Submodular Minimiz…
We investigate the performance of a deterministic GREEDY algorithm for the problem of maximizing functions under a partition matroid constraint. We consider non-monotone submodular functions and monotone subadditive functions. Even though…
This paper discusses a special kind of convex constrained optimization problem, whose constraints consist of box inequalities and linear equalities. For this problem, in addition to general optimization algorithms such as exact penalty…
Energy minimization has been an intensely studied core problem in computer vision. With growing image sizes (2D and 3D), it is now highly desirable to run energy minimization algorithms in parallel. But many existing algorithms, in…
We introduce a particular optimization problem that minimizes the sum of a non-convex quadratic function and logarithmic barrier-functions in a $\ell_\infty$-trust-region (i.e. cube). Our paper covers three topics. We explain the relevance…
We consider a problem of optimizing convex functionals over matroid bases. It is richly expressive and captures certain quadratic assignment and clustering problems. While generally NP-hard, we show it is polynomial time solvable when a…
A wide variety of problems in machine learning, including exemplar clustering, document summarization, and sensor placement, can be cast as constrained submodular maximization problems. A lot of recent effort has been devoted to developing…
Let $D$ be a directed graph cellularly embedded in a surface together with non-negative cost on its arcs. Given any integer circulation in $D$, we study the problem of finding a minimum-cost non-negative integer circulation in $D$ that is…
We study the problem of maximizing a monotone submodular function with viability constraints. This problem originates from computational biology, where we are given a phylogenetic tree over a set of species and a directed graph, the…
We propose a proximal approach to deal with a class of convex variational problems involving nonlinear constraints. A large family of constraints, proven to be effective in the solution of inverse problems, can be expressed as the lower…
We consider the problem of minimizing a sum of non-convex functions over a compact domain, subject to linear inequality and equality constraints. Approximate solutions can be found by solving a convexified version of the problem, in which…
In this survey we consider polynomial optimization problems, asking to minimize a polynomial function over a compact semialgebraic set, defined by polynomial inequalities. This models a great variety of (in general, nonlinear nonconvex)…
In this paper we consider non-smooth convex optimization problems with (possibly) infinite intersection of constraints. In contrast to the classical approach, where the constraints are usually represented as intersection of simple sets,…
In this paper, we present an algorithm for minimizing the difference between two submodular functions using a variational framework which is based on (an extension of) the concave-convex procedure [17]. Because several commonly used metrics…
Submodular functions have been studied extensively in machine learning and data mining. In particular, the optimization of submodular functions over the integer lattice (integer submodular functions) has recently attracted much interest,…
Variational inequalities play a key role in machine learning research, such as generative adversarial networks, reinforcement learning, adversarial training, and generative models. This paper is devoted to the constrained variational…
In this paper, we consider the problem of distributed optimisation of a separable convex cost function over a graph, where every edge and node in the graph could carry both linear equality and/or inequality constraints. We show how to…
We consider the problem of approximating the solution of variational problems subject to the constraint that the admissible functions must be convex. This problem is at the interface between convex analysis, convex optimization, variational…
Motivated by modern regression applications, in this paper, we study the convexification of a class of convex optimization problems with indicator variables and combinatorial constraints on the indicators. Unlike most of the previous work…
In this paper we derive strong linear inequalities for sets of the form {(x, q) \in Rd \times R : q \geq Q(x), x \in Rd - int(P)}, where Q(x) : Rd \rightarrow R is a quadratic function, P \subset Rd and "int" denotes interior. Of particular…
In this paper, we investigate a class of submodular problems which in general are very hard. These include minimizing a submodular cost function under combinatorial constraints, which include cuts, matchings, paths, etc., optimizing a…