We consider the problem of finding the best approximation point from a polyhedral set, and its applications, in particular to solving large-scale linear programs. The classical projection problem has many various and many applications. We study a regularized nonsmooth Newton type solution method where the Jacobian is singular; and we compare the computational performance to … Read more
In this paper, we investigate the problem of finding a robust baseline schedule for the project scheduling problem under uncertain process times. We assume that the probability distribution for the duration is unknown but an estimation together with an interval in which this time can vary is given. At most $ \Gamma $ of the … Read more
For over ten years, the constraint integer programming framework SCIP has been extended by capabilities for the solution of convex and nonconvex mixed-integer nonlinear programs (MINLPs). With the recently published version 8.0, these capabilities have been largely reworked and extended. This paper discusses the motivations for recent changes and provides an overview of features that … Read more
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Markov decision process (MDP) is a decision making framework where a decision maker is interested in maximizing the expected discounted value of a stream of rewards received at future stages at various states which are visited according to a controlled Markov chain. Many algorithms including linear programming methods are available in the literature to compute … Read more
Multiobjective quadratic programs (MOQPs) are appealing since convex quadratic programs have elegant mathematical properties and model important applications. Adding mixed-integer variables extends their applicability while the resulting programs become global optimization problems. We design and implement a branch and bound (BB) algorithm for biobjective mixed-integer quadratic programs (BOMIQPs). In contrast to the existing algorithms in … Read more
Mixed-integer optimal control problems arise in many practical applications combining nonlinear, dynamic, and combinatorial features. To cope with the resulting complexity, several approaches have been suggested in the past. Some of them rely on solving a reformulated and relaxed control problem, referred to as partial outer convexification. Inspired by an efficient algorithm for switching time … Read more
The vehicle routing problem with stochastic demands (VRPSD) is a well studied variant of the classic (deterministic) capacitated vehicle routing problem (CVRP) where the customer demands are given by random variables. Two prominent approaches for solving the VRPSD model it either as a chance-constraint program (CC-VRPSD) or as a two-stage stochastic program (2S-VRPSD). In this … Read more
Wasserstein distributionally robust optimization (DRO) has found success in operations research and machine learning applications as a powerful means to obtain solutions with favourable out-of-sample performances. Two compelling explanations for the success are the generalization bounds derived from Wasserstein DRO and the equivalency between Wasserstein DRO and the regularization scheme commonly applied in machine learning. … Read more
Symmetry handling is a key technique for reducing the running time of branch-and-bound methods for solving mixed-integer linear programs. In this paper, we generalize the notion of (permutation) symmetries to mixed-integer semidefinite programs (MISDPs). We first discuss how symmetries of MISDPs can be automatically detected by finding automorphisms of a suitably colored auxiliary graph. Then … Read more