Improving Benders decomposition via a non-linear cut selection procedure

A non-linear lifting procedure is proposed to generate high density Benders cuts. The new denser cuts cover more master problem variables than traditional Benders cuts, shortening the required number of iterations to reach optimality, and speeding up the Benders decomposition algorithm. To lessen the intricacy stemmed from the non-linearity, a simple outer approximation lineariza- tion … Read more

Formulations and Decomposition Methods for the Incomplete Hub Location Problem With and Without Hop-Constraints

The incomplete hub location problem with and without hop-constraints is modeled using a Leontief substitution system approach. The Leontief formalism provides a set of important theoretical properties and delivers formulations with tight linear bounds that can explicitly incorporate hop constraints for each origin-destination pair of demands. Furthermore, the proposed formulations are amenable to a Benders … Read more

Asymptotical Analysis of a SAA Estimator for Optimal Value of a Two Stage Problem with Quadratic Recourse

In this paper, we first consider the stability analysis of a convex quadratic programming problem and its restricted Wolfe dual in which all parameters in the problem are perturbed. We demonstrate the upper semi-continuity of solution mappings for the primal problem and the restricted Wolfe dual problem and establish the Hadamard directionally differentiability of the … Read more

Strengthened MILP Formulation for Combined-Cycle Units

Due to the increased utilization of gas-fired combined-cycle units for power generation in the U.S., accurate and computationally efficient models are more and more needed. The recently proposed edge-based formulation for combined-cycle units helps accurately describe the operations of combined-cycle units including capturing the transition processes and physical constraints for each turbine. In this paper, … Read more

On the polyhedrality of closures of multi-branch split sets and other polyhedra with bounded max-facet-width

For a fixed integer $t > 0$, we say that a $t$-branch split set (the union of $t$ split sets) is dominated by another one on a polyhedron $P$ if all cuts for $P$ obtained from the first $t$-branch split set are implied by cuts obtained from the second one. We prove that given a … Read more

Exploiting Problem Structure in Optimization under Uncertainty via Online Convex Optimization

In this paper, we consider two paradigms that are developed to account for uncertainty in optimization models: robust optimization (RO) and joint estimation-optimization (JEO). We examine recent developments on efficient and scalable iterative first-order methods for these problems, and show that these iterative methods can be viewed through the lens of online convex optimization (OCO). … Read more

Constructing New Weighted l1-Algorithms for the Sparsest Points of Polyhedral Sets

The l0-minimization problem that seeks the sparsest point of a polyhedral set is a longstanding challenging problem in the fields of signal and image processing, numerical linear algebra and mathematical optimization. The weighted l1-method is one of the most plausible methods for solving this problem. In this paper, we develop a new weighted l1-method through … Read more