相关论文: Approximation by analytic matrix functions. The fo…

Symmetric submodular functions are an important family of submodular functions capturing many interesting cases including cut functions of graphs and hypergraphs. Maximization of such functions subject to various constraints receives little…

Maximizing a single submodular set function subject to a cardinality constraint is a well-studied and central topic in combinatorial optimization. However, finding a set that maximizes multiple functions at the same time is much less…

We design a sublinear-time approximation algorithm for quadratic function minimization problems with a better error bound than the previous algorithm by Hayashi and Yoshida (NIPS'16). Our approximation algorithm can be modified to handle…

We consider the semi-infinite optimization problem: $f^*:=\min_{x\in X}\:\{f(x): g(x,y)\,\leq \,0,\:\forally\in Y_x\}$, where $f,g$ are polynomials and $X\subset R^n$ as well as $Y_\x\subset R^p$, $x\in X$, are compact basic semi-algebraic…

Semi-supervised clustering is a basic problem in various applications. Most existing methods require knowledge of the ideal cluster number, which is often difficult to obtain in practice. Besides, satisfying the must-link constraints is…

This paper studies simple bilevel problems, where a convex upper-level function is minimized over the optimal solutions of a convex lower-level problem. We first show the fundamental difficulty of simple bilevel problems, that the…

Wall-clock-time is minimized for a solution to a linear-program with block-diagonal-structure, by decomposing the linear-program into as many small-sized subproblems as possible, each block resulting in a separate subproblem, when the…

The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality…

In this work, we study the classical problem of maximizing a submodular function subject to a matroid constraint. We develop deterministic algorithms that are very parsimonious with respect to querying the submodular function, for both the…

This paper introduces an efficient algorithm for computing the best approximation of a given matrix onto the intersection of linear equalities, inequalities and the doubly nonnegative cone (the cone of all positive semidefinite matrices…

We formalize the problem of selecting the optimal set of options for planning as that of computing the smallest set of options so that planning converges in less than a given maximum of value-iteration passes. We first show that the problem…

Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…

We study the best approximation problem: \[ \displaystyle \min_{\alpha\in \mathbb R^m}\max_{1\leq i\leq n}\left|y_i -\sum_{j=1}^m \alpha_j \Gamma_j ({\bf x}_i) \right|. \] Here: $\Gamma:=\left\{\Gamma_1,...,\Gamma_m\right\}$ is a list of…

We propose the {\alpha}-suboptimal covering number to characterize multi-task control problems where the set of dynamical systems and/or cost functions is infinite, analogous to the cardinality of finite task sets. This notion may help…

In this paper, we investigate the butterfly factorization problem, i.e., the problem of approximating a matrix by a product of sparse and structured factors. We propose a new formal mathematical description of such factors, that encompasses…

Matrix rank minimization problems are gaining a plenty of recent attention in both mathematical and engineering fields. This class of problems, arising in various and across-discipline applications, is known to be NP-hard in general. In…

Balkanski and Singer [5] recently initiated the study of adaptivity (or parallelism) for constrained submodular function maximization, and studied the setting of a cardinality constraint. Very recent improvements for this problem by…

In this paper, we introduce the Maximum Matrix Contraction problem, where we aim to contract as much as possible a binary matrix in order to maximize its density. We study the complexity and the polynomial approximability of the problem.…

We study the problem of maximizing a function that is approximately submodular under a cardinality constraint. Approximate submodularity implicitly appears in a wide range of applications as in many cases errors in evaluation of a…

We present an optimization problem emerging from optimal control theory and situated at the intersection of fractional programming and linear max-min programming on polytopes. A na\"ive solution would require solving four nested, possibly…