The goal of this paper is to study the effect of inexact first-order information on the first-order methods designed for smooth strongly convex optimization problems. We introduce the notion of (delta,L,mu)-oracle, that can be seen as an extension of the inexact (delta,L)-oracle previously introduced, taking into account strong convexity. We consider different examples of (delta,L,mu)-oracle: … Read more
We propose a new family of subgradient- and gradient-based methods which converges with optimal complexity for convex optimization problems whose feasible region is simple enough. This includes cases where the objective function is non-smooth, smooth, have composite/saddle structure, or are given by an inexact oracle model. We unified the way of constructing the subproblems which … Read more
We study a number of variants of an abstract scheduling problem inspired by the scheduling of reclaimers in the stockyard of a coal export terminal. We analyze the complexity of each of the variants, providing complexity proofs for some and polynomial algorithms for others. For one, especially interesting variant, we also develop a constant factor … Read more
We present a novel framework, namely AADMM, for acceleration of linearized alternating direction method of multipliers (ADMM). The basic idea of AADMM is to incorporate a multi-step acceleration scheme into linearized ADMM. We demonstrate that for solving a class of convex composite optimization with linear constraints, the rate of convergence of AADMM is better than … Read more
This paper presents an algorithm for approximately minimizing a convex function in simple, not necessarily bounded convex domains, assuming only that function values and subgradients are available. No global information about the objective function is needed apart from a strong convexity parameter (which can be put to zero if only convexity is known). The worst … Read more
In this paper, we present an inexact block-decomposition (BD) first-order method for solving standard form conic semidefinite programming (SDP) which avoids computations of exact projections onto the manifold defined by the affine constraints and, as a result, is able to handle extra large SDP instances. The method is based on a two-block reformulation of the … Read more
This article considers the two-player composite Nash equilibrium (CNE) problem with a separable non-smooth part, which is known to include the composite saddle-point (CSP) problem as a special case. Due to its two-block structure, this problem can be solved by any algorithm belonging to the block-decomposition hybrid proximal-extragradient (BD-HPE) framework. The framework consists of a … Read more
In this paper, we generalize the well-known Nesterov’s accelerated gradient (AG) method, originally designed for convex smooth optimization, to solve nonconvex and possibly stochastic optimization problems. We demonstrate that by properly specifying the stepsize policy, the AG method exhibits the best known rate of convergence for solving general nonconvex smooth optimization problems by using first-order … Read more
In this paper we show that the infinite-dimensional differential games with simple objective functional can be solved in a finite-dimensional dual form in the space of dual multipliers for the constraints related to the end points of the trajectories. The primal solutions can be easily reconstructed by the appropriate dual subgradient schemes. The suggested schemes … Read more
In this paper we address a deterministic scheduling problem in which two agents compete for the usage of a single machine. Each agent decides on a fixed order to submit its tasks to an external coordination subject, who sequences them according to a known priority rule. We consider the problem from different perspectives. First, we … Read more