Decomposition Algorithms for Two-Stage Distributionally Robust Mixed Binary Programs

In this paper, we introduce and study a two-stage distributionally robust mixed binary problem (TSDR-MBP) where the random parameters follow the worst-case distribution belonging to an uncertainty set of probability distributions. We present a decomposition algorithm, which utilizes distribution separation procedure and parametric cuts within Benders’ algorithm or L-shaped method, to solve TSDR-MBPs with binary … Read more

Demand Modeling in the Presence of Unobserved Lost Sales

We present an integrated optimization approach to parameter estimation for discrete choice demand models where data for one or more choice alternatives are censored. We employ a mixed-integer program (MIP) to jointly determine the prediction parameters associated with the customer arrival rate and their substitutive choices. This integrated approach enables us to recover proven, (near-) … Read more

QPLIB: A Library of Quadratic Programming Instances

This paper describes a new instance library for Quadratic Programming (QP), i.e., the family of continuous and (mixed)-integer optimization problems where the objective function, the constrains, or both are quadratic. QP is a very “varied” class of problems, comprising sub-classes of problems ranging from trivial to undecidable. Solution methods for QP are very diverse, ranging … Read more

Optimization Techniques for Tree-Structured Nonlinear Problems

Robust model predictive control approaches and other applications lead to nonlinear optimization problems defined on (scenario) trees. We present structure-preserving Quasi-Newton update formulas as well as structured inertia correction techniques that allow to solve these problems by interior-point methods with specialized KKT solvers for tree-structured optimization problems. The same type of KKT solvers could be … Read more

Convergence rate bounds for a proximal ADMM with over-relaxation stepsize parameter for solving nonconvex linearly constrained problems

This paper establishes convergence rate bounds for a variant of the proximal alternating direction method of multipliers (ADMM) for solving nonconvex linearly constrained optimization problems. The variant of the proximal ADMM allows the inclusion of an over-relaxation stepsize parameter belonging to the interval (0,2). To the best of our knowledge, all related papers in the … Read more