We present a novel formulation for startup cost computation in the unit commitment problem (UC). Both the proposed formulation and existing formulations in the literature are placed in a formal, theoretical dominance hierarchy based on their respective linear programming relaxations. The proposed formulation is tested empirically against existing formulations on large-scale unit commitment instances drawn … Read more
The SCIP Optimization Suite is a powerful collection of optimization software that consists of the branch-cut-and-price framework and mixed-integer programming solver SCIP, the linear programming solver SoPlex, the modeling language Zimpl, the parallelization framework UG, and the generic branch-cut-and-price solver GCG. Additionally, it features the extensions SCIP-Jack for solving Steiner tree problems, PolySCIP for solving … Read more
Alternating current optimal power flow (AC OPF) is one of the most fundamental optimization problems in electrical power systems. It can be formulated as a semidefinite program (SDP) with rank constraints. Solving AC OPF, that is, obtaining near optimal primal solutions as well as high quality dual bounds for this non-convex program, presents a major … Read more
In this paper, we propose a semi-metric for Markov processes that allows to bound optimal values of linear Markov Decision Processes (MDPs). Similar to existing notions of distance for general stochastic processes our distance is based on transportation metrics. Apart from the specialization to MDPs, our contribution is to make the distance problem specific, i.e., … Read more
An important problem in the breeding of livestock, crops, and forest trees is the optimum of selection of genotypes that maximizes genetic gain. The key constraint in the optimal selection is a convex quadratic constraint that ensures genetic diversity, therefore, the optimal selection can be cast as a second-order cone programming (SOCP) problem. Yamashita et … Read more
The generalized intersection cut (GIC) paradigm is a recent framework for generating cutting planes in mixed integer programming with attractive theoretical properties. We investigate this computationally unexplored paradigm and observe that a key hyperplane activation procedure embedded in it is not computationally viable. To overcome this issue, we develop a novel replacement to this procedure … Read more
Efficient management of operations in seaport container terminals has become a critical issue, due to the increase in maritime traffic and the strong competition between ports. In this paper we focus on two seaside operational problems: the Berth Allocation Problem and the Quay Crane Assignment Problem, which are considered in an integrated way. For the … Read more
The sparse bounded degree sum-of-squares (sparse-BSOS) hierarchy of Weisser, Lasserre and Toh [arXiv:1607.01151,2016] constructs a sequence of lower bounds for a sparse polynomial optimization problem. Under some assumptions, it is proven by the authors that the sequence converges to the optimal value. In this paper, we modify the hierarchy to deal with problems containing equality … Read more
Generalized matrix-fractional (GMF) functions are a class of matrix support functions introduced by Burke and Hoheisel as a tool for unifying a range of seemingly divergent matrix optimization problems associated with inverse problems, regularization and learning. In this paper we dramatically simplify the support function representation for GMF functions as well as the representation of … Read more
We use Markov risk measures to formulate a risk averse version of a total cost problem on a controlled Markov process in infinite horizon. The one step costs are in $L^1$ but not necessarily bounded. We derive the conditions for the existence of the optimal strategies and present the robust dynamic programming equations. We illustrate … Read more