New Multirectional Mean Value Inequality
We establish new and stronger inequality of Clarke-Ledyaev type by direct construction. CitationPreprint, 2017, Sofia University ArticleDownload View PDF
A Stochastic Programming Approach for Electric Vehicle Charging Network Design
Advantages of electric vehicles (EV) include reduction of greenhouse gas and other emissions, energy security, and fuel economy. The societal benefits of large-scale adoption of EVs cannot be realized without adequate deployment of publicly accessible charging stations. We propose a two-stage stochastic programming model to determine the optimal network of charging stations for a community … Read more
Two-stage Stochastic Programming under Multivariate Risk Constraints with an Application to Humanitarian Relief Network Design
In this study, we consider two classes of multicriteria two-stage stochastic programs in finite probability spaces with multivariate risk constraints. The first-stage problem features a multivariate stochastic benchmarking constraint based on a vector-valued random variable representing multiple and possibly conflicting stochastic performance measures associated with the second-stage decisions. In particular, the aim is to ensure … Read more
Distributionally Robust Reward-risk Ratio Programming with Wasserstein Metric
Reward-risk ratio (RR) is a very important stock market definition. In recent years, people extend RR model as distributionally robust reward-risk ratio (DRR) to capture the situation that the investor does not have complete information on the distribution of the underlying uncertainty. In this paper, we study the DRR model where the ambiguity on the … Read more
An approximation algorithm for the partial covering 0-1 integer program
The partial covering 0-1 integer program (PCIP) is a relaxed problem of the covering 0-1 integer program (CIP) such that some fixed number of constraints may not be satisfied. This type of relaxation is also discussed in the partial set multi-cover problem (PSMCP) and the partial set cover problem (PSCP). In this paper, we propose … Read more
Optimal Price Zones of Electricity Markets: A Mixed-Integer Multilevel Model and Global Solution Approaches
Mathematical modeling of market design issues in liberalized electricity markets often leads to mixed-integer nonlinear multilevel optimization problems for which no general-purpose solvers exist and which are intractable in general. In this work, we consider the problem of splitting a market area into a given number of price zones such that the resulting market design … Read more
The Robust Uncapacitated Lot Sizing Model with Uncertainty Range
We study robust versions of the uncapacitated lot sizing problem, where the demand is subject to uncertainty. The robust models are guided by three parameters, namely, the total scaled uncertainty budget, the minimum number of periods in which one would like the demand to be protected against uncertainty, and the minimum scaled protection level per … Read more
Geometric descent method for convex composite minimization
In this paper, we extend the geometric descent method recently proposed by Bubeck, Lee and Singh to tackle nonsmooth and strongly convex composite problems. We prove that our proposed algorithm, dubbed geometric proximal gradient method (GeoPG), converges with a linear rate $(1-1/\sqrt{\kappa})$ and thus achieves the optimal rate among first-order methods, where $\kappa$ is the … Read more
Complexity Analysis of a Trust Funnel Algorithm for Equality Constrained Optimization
A method is proposed for solving equality constrained nonlinear optimization problems involving twice continuously differentiable functions. The method employs a trust funnel approach consisting of two phases: a first phase to locate an $\epsilon$-feasible point and a second phase to seek optimality while maintaining at least $\epsilon$-feasibility. A two-phase approach of this kind based on … Read more
Fooling Sets and the Spanning Tree Polytope
In the study of extensions of polytopes of combinatorial optimization problems, a notorious open question is that for the size of the smallest extended formulation of the Minimum Spanning Tree problem on a complete graph with n nodes. The best known lower bound is \Omega(n^2), the best known upper bound is O(n^3). In this note … Read more