相关论文: When can $l_p$-norm objective functions be minimiz…

The optimization of submodular functions on the integer lattice has received much attention recently, but the objective functions of many applications are non-submodular. We provide two approximation algorithms for maximizing a…

An online decision-making problem is a learning problem in which a player repeatedly makes decisions in order to minimize the long-term loss. These problems that emerge in applications often have nonlinear combinatorial objective functions,…

Recently, $l_{2,1}$ matrix norm has been widely applied to many areas such as computer vision, pattern recognition, biological study and etc. As an extension of $l_1$ vector norm, the mixed $l_{2,1}$ matrix norm is often used to find…

Recently, it has become evident that submodularity naturally captures widely occurring concepts in machine learning, signal processing and computer vision. Consequently, there is need for efficient optimization procedures for submodular…

We study an abstract setting for cutting planes for integer programming called the infinite group problem. In this abstraction, cutting planes are computed via cut generating function that act on the simplex tableau. In this function space,…

Can one reduce the size of a graph without significantly altering its basic properties? The graph reduction problem is hereby approached from the perspective of restricted spectral approximation, a modification of the spectral similarity…

Mathematical optimization is widely used in various research fields. With a carefully-designed objective function, mathematical optimization can be quite helpful in solving many problems. However, objective functions are usually…

Robust optimization is becoming increasingly important in machine learning applications. In this paper, we study a unified framework of robust submodular optimization. We study this problem both from a minimization and maximization…

We define the supermodular rank of a function on a lattice. This is the smallest number of terms needed to decompose it into a sum of supermodular functions. The supermodular summands are defined with respect to different partial orders. We…

This paper presents the first combinatorial polynomial-time algorithm for minimizing submodular set functions, answering an open question posed in 1981 by Grotschel, Lovasz, and Schrijver. The algorithm employs a scaling scheme that uses a…

We study the problem of minimizing a convex function on a nonempty, finite subset of the integer lattice when the function cannot be evaluated at noninteger points. We propose a new underestimator that does not require access to…

We consider submodular function minimization in the oracle model: given black-box access to a submodular set function $f:2^{[n]}\rightarrow \mathbb{R}$, find an element of $\arg\min_S \{f(S)\}$ using as few queries to $f(\cdot)$ as…

We consider the problem of minimizing the makespan on batch processing identical machines, subject to compatibility constraints, where two jobs are compatible if they can be processed simultaneously in a same batch. These constraints are…

We design new approximation algorithms for the problems of optimizing submodular and supermodular functions subject to a single matroid constraint. Specifically, we consider the case in which we wish to maximize a nondecreasing submodular…

Given a graph $G=(V,E)$ with two distinguished vertices $s,t\in V$ and an integer parameter $L>0$, an {\em $L$-bounded cut} is a subset $F$ of edges (vertices) such that the every path between $s$ and $t$ in $G\setminus F$ has length more…

The problem of objectively choosing a string of actions to optimize an objective function that is string submodular has been considered in [1]. There it is shown that the greedy strategy, consisting of a string of actions that only locally…

In numerous substitution models for the $\l_{0}$-norm minimization problem $(P_{0})$, the $\l_{p}$-norm minimization $(P_{p})$ with $0<p<1$ have been considered as the most natural choice. However, the non-convex optimization problem…

We consider the problem of maximizing non-negative non-decreasing set functions. Although most of the recent work focus on exploiting submodularity, it turns out that several objectives we encounter in practice are not submodular.…

Most state-of-the-art motion segmentation algorithms draw their potential from modeling motion differences of local entities such as point trajectories in terms of pairwise potentials in graphical models. Inference in instances of minimum…

We propose a method to conduct uniform inference for the (optimal) value function, that is, the function that results from optimizing an objective function marginally over one of its arguments. Marginal optimization is not Hadamard…