Related papers: Efficient Convex Optimization with Membership Orac…
We develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial…
We propose a general solution approach for min-max-robust counterparts of combinatorial optimization problems with uncertain linear objectives. We focus on the discrete scenario case, but our approach can be extended to other types of…
We present two first-order, sequential optimization algorithms to solve constrained optimization problems. We consider a black-box setting with a priori unknown, non-convex objective and constraint functions that have Lipschitz continuous…
In this paper, we provide tight lower bounds for the oracle complexity of minimizing high-order H\"older smooth and uniformly convex functions. Specifically, for a function whose $p^{th}$-order derivatives are H\"older continuous with…
In this paper some adaptive mirror descent algorithms for problems of minimization convex objective functional with several convex Lipschitz (generally, non-smooth) functional constraints are considered. It is shown that the methods are…
We show that any memory-constrained, first-order algorithm which minimizes $d$-dimensional, $1$-Lipschitz convex functions over the unit ball to $1/\mathrm{poly}(d)$ accuracy using at most $d^{1.25 - \delta}$ bits of memory must make at…
We study the min-max optimization problem where each function contributing to the max operation is strongly-convex and smooth with bounded gradient in the search domain. By smoothing the max operator, we show the ability to achieve an…
Robust optimization is a common framework in optimization under uncertainty when the problem parameters are not known, but it is rather known that the parameters belong to some given uncertainty set. In the robust optimization framework the…
Finding multiple solutions of non-convex optimization problems is a ubiquitous yet challenging task. Most past algorithms either apply single-solution optimization methods from multiple random initial guesses or search in the vicinity of…
This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…
In this work, we propose a method for minimizing non-convex functions with Lipschitz continuous $p$th-order derivatives, starting from $p \geq 1$. The method, however, only requires derivative information up to order $(p-1)$, since the…
This article proposes a new discrete framework for approximating solutions to shape optimization problems under convexity constraints. The numerical method, based on the support function or the gauge function, is guaranteed to generate…
In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz…
Consider a set $P \subseteq \Re^d$ of $n$ points, and a convex body $C$ provided via a separation oracle. The task at hand is to decide for each point of $P$ if it is in $C$ using the fewest number of oracle queries. We show that one can…
We consider sum-type strongly convex optimization problem (first term) with smooth convex not proximal friendly composite (second term). We show that the complexity of this problem can be split into optimal number of incremental oracle…
We consider online resource allocation problems where given a set of requests our goal is to select a subset that maximizes a value minus cost type of objective function. Requests are presented online in random order, and each request…
We propose a family of recursive cutting-plane algorithms to solve feasibility problems with constrained memory, which can also be used for first-order convex optimization. Precisely, in order to find a point within a ball of radius…
Two new optimization techniques based on projections onto convex space (POCS) framework for solving convex and some non-convex optimization problems are presented. The dimension of the minimization problem is lifted by one and sets…
We consider minimization of a smooth nonconvex function with inexact oracle access to gradient and Hessian (without assuming access to the function value) to achieve approximate second-order optimality. A novel feature of our method is that…
An algorithm which computes a solution of a set optimization problem is provided. The graph of the objective map is assumed to be given by finitely many linear inequalities. A solution is understood to be a set of points in the domain…