It is shown how to use the performance and data profile benchmarking tools to improve algorithms’ performance. An illustration for the BFO derivative-free optimizer suggests that the obtained gains are potentially significant. CitationACM Transactions on Mathematical Software, 45:2 (2019), Article 20.ArticleDownload View PDF
Given a non-convex twice continuously differentiable cost function with Lipschitz continuous gradient, we prove that all of the block coordinate gradient descent, block mirror descent and proximal block coordinate descent methods converge to stationary points satisfying the second-order necessary condition, almost surely with random initialization. All our results are ascribed to the center-stable manifold theorem … Read more
We consider an n-player non-cooperative game with random payoffs and continuous strategy set for each player. The random payoffs of each player are defined using a finite dimensional random vector. We formulate this problem as a chance-constrained game by defining the payoff function of each player using a chance constraint. We first consider the case … Read more
In this paper, we consider the two-stage extension of the one-dimensional cutting stock problem which arises when technical requirements inhibit the cutting of large stock rolls to demanded widths of finished rolls directly. Therefore, the demands on finished rolls are fulfilled through two subsequent cutting processes, in which the rolls produced in the former are … Read more
Chance constrained programming, quantile/Value-at-Risk (VaR) optimization and integral quantile / Conditional Value-at-Risk (CVaR) optimization problems as Stochastic Programming Problems with Probability Functions (SPP-PF) are one of the most widely studied optimization problems in recent years. As a rule real-life SPP-PF is nonsmooth nonconvex optimization problem with complex geometry of objective function. Moreover, often it cannot … Read more
We study the existence and uniqueness of equilibria for perfectly competitive markets in capacitated transport networks. The model under consideration is rather general so that it captures basic aspects of related models in, e.g., gas or electricity networks. We formulate the market equilibrium model as a mixed complementarity problem and show the equivalence to a … Read more
This work is about active set identification strategies aimed at accelerating block-coordinate descent methods (BCDM) applied to large-scale problems. We start by devising an identification function tailored for bound-constrained composite minimization together with an associated version of the BCDM, called Active BCDM, that is also globally convergent. The identification function gives rise to an efficient … Read more
In this work, we give a tight estimate of the rate of convergence for the Halpern-Iteration for approximating a fixed point of a nonexpansive mapping in a Hilbert space. Specifically, we prove that the norm of the residuals is upper bounded by the distance of the initial iterate to the closest fixed point divided by … Read more
In the analysis of complex stochastic dynamic programs, we often seek strong theoretical guarantees on the suboptimality of heuristic policies. One technique for obtaining performance bounds is perfect information analysis: this approach provides bounds on the performance of an optimal policy by considering a decision maker who has access to the outcomes of all future … Read more
The direct extension of the classic alternating direction method with multipliers (ADMMe) to the multi-block separable convex optimization problem is not necessarily convergent, though it often performs very well in practice. In order to preserve the numerical advantages of ADMMe and obtain convergence, many modified ADMM were proposed by correcting the output of ADMMe or … Read more