Related papers: Minimizing a low-dimensional convex function over …

In the first part of this paper we introduced an algorithm that uses reachable set approximation to approximate the minimum time function of linear control problems. To illustrate the error estimates and to demonstrate differences to other…

We propose a conditional gradient framework for a composite convex minimization template with broad applications. Our approach combines smoothing and homotopy techniques under the CGM framework, and provably achieves the optimal…

Submodular set-functions have many applications in combinatorial optimization, as they can be minimized and approximately maximized in polynomial time. A key element in many of the algorithms and analyses is the possibility of extending the…

Let $(L; \sqcap, \sqcup)$ be a finite lattice and let $n$ be a positive integer. A function $f : L^n \to \mathbb{R}$ is said to be submodular if $f(\tup{a} \sqcap \tup{b}) + f(\tup{a} \sqcup \tup{b}) \leq f(\tup{a}) + f(\tup{b})$ for all…

We study the optimal lower and upper complexity bounds for finding approximate solutions to the composite problem $\min_x\ f(x)+h(Ax-b)$, where $f$ is smooth and $h$ is convex. Given access to the proximal operator of $h$, for strongly…

Random projection (RP) is a classical technique for reducing storage and computational costs. We analyze RP-based approximations of convex programs, in which the original optimization problem is approximated by the solution of a…

We consider the problem of minimizing a composite convex function with two different access methods: an oracle, for which we can evaluate the value and gradient, and a structured function, which we access only by solving a convex…

We consider minimization of composite functions of the form $f(g(x))+h(x)$, where $f$ and $h$ are convex functions (which can be nonsmooth) and $g$ is a smooth vector mapping. In addition, we assume that $g$ is the average of finite number…

We consider the graph $k$-partitioning problem under the min-max objective, termed as Minmax $k$-cut. The input here is a graph $G=(V,E)$ with non-negative edge weights $w:E\rightarrow \mathbb{R}_+$ and an integer $k\geq 2$ and the goal is…

Submodular function minimization (SFM) is a fundamental discrete optimization problem which generalizes many well known problems, has applications in various fields, and can be solved in polynomial time. Owing to applications in computer…

Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…

In this paper we consider convex optimization problems with stochastic composite objective function subject to (possibly) infinite intersection of constraints. The objective function is expressed in terms of expectation operator over a sum…

This paper propose a new frame work for finding global minima which we call optimization by cut. In each iteration, it takes some samples from the feasible region and evaluates the objective function at these points. Based on the…

We investigate how to solve smooth matrix optimization problems with general linear inequality constraints on the eigenvalues of a symmetric matrix. We present solution methods to obtain exact global minima for linear objective functions,…

We provide new insight into the convergence properties of the Douglas-Rachford algorithm for the problem $\min_x \{f(x)+g(x)\}$, where $f$ and $g$ are convex functions. Our approach relies on and highlights the natural primal-dual symmetry…

We study the approximation of measurable functions on the hypercube by functions arising from affine neural networks. Our main achievement is an approximation of any measurable function $f \colon W_n \to [-1,1]$ up to a prescribed precision…

We introduce a class of stochastic algorithms for minimizing weakly convex functions over proximally smooth sets. As their main building blocks, the algorithms use simplified models of the objective function and the constraint set, along…

We study dual-based algorithms for distributed convex optimization problems over networks, where the objective is to minimize a sum $\sum_{i=1}^{m}f_i(z)$ of functions over in a network. We provide complexity bounds for four different…

We consider the problem of minimizing the composition of a nonsmooth function with a smooth mapping in the case where the proximity operator of the nonsmooth function can be explicitly computed. We first show that this proximity operator…

Given a matrix-valued function $\mathcal{F}(\lambda)=\sum_{i=1}^d f_i(\lambda) A_i$, with complex matrices $A_i$ and $f_i(\lambda)$ entire functions for $i=1,\ldots,d$, we discuss a method for the numerical approximation of the distance to…