While semidefinite programming (SDP) problems are polynomially solvable in theory, it is often difficult to solve large SDP instances in practice. One technique to address this issue is to relax the global positive-semidefiniteness (PSD) constraint and only enforce PSD-ness on smaller k times k principal submatrices — we call this the sparse SDP relaxation. Surprisingly, … Read more
Quantum Bridge Analytics relates to methods and systems for hybrid classical-quantum computing, and is devoted to developing tools for bridging classical and quantum computing to gain the benefits of their alliance in the present and enable enhanced practical application of quantum computing in the future. This is the second of a two-part tutorial that surveys … Read more
In \cite{siebert2019linear} the authors present a set of integer programs (IPs) for the Steiner tree problem, which can be used for both, the directed and the undirected setting of the problem. Each IP finds an optimal Steiner tree with a specific structure. A solution with the lowest cost, corresponds to an optimal solution to the … Read more
In the absence of direct demand-side bids for certain reliability products in the wholesale electricity markets, Independent System Operators (ISOs) traditionally use fixed demand requirements with penalty factors to clear the market. This approach does not allow proper tradeoffs between reliability and cost due to the inelasticity of the fixed requirements. Therefore, ISOs have been … Read more
We consider a generic class of chance-constrained optimization problems with heavy-tailed (i.e., power-law type) risk factors. In this setting, we use the scenario approach to obtain a constant approximation to the optimal solution with a computational complexity that is uniform in the risk tolerance parameter. We additionally illustrate the efficiency of our algorithm in the … Read more
Problem definition: Bargaining situations are ubiquitous in economics and management. We consider the problem of bargaining for a fair ex-ante distribution of random profits arising from a cooperative effort of a fixed set of risk-averse agents. Our approach integrates optimal managerial decision making into bargaining situations with random outcomes and explicitly models the impact of … Read more
We study the Knapsack Problem with Conflict Graph (KPCG), a generalization of the Knapsack Problem in which a conflict graph specifies pairs of items (vertices of the graph) which cannot be simultaneously selected in a solution. The KPCG asks for determining a maximum-profit subset of items of total weight no larger than the knapsack capacity … Read more
In this paper, we present a method for generating scenarios by selection from historical data. We start with two models for a univariate single-period case and then extend the better-performing one to the case of selecting sequences of multivariate data. We then test the method on data series for wind- and solar-power generation in Scandinavia. … Read more
Updating the augmented Lagrangian multiplier by closed-form expression yields efficient first-order infeasible approach for optimization problems with orthogonality constraints. Hence, parallelization becomes tractable in solving this type of problems. Inspired by this closed-form updating scheme, we propose an exact penalty function model with compact convex constraints (PenC). We show that PenC can act as an … Read more
JuMP is an open-source algebraic modeling language in the Julia language. In this work, we discuss a complete re-write of JuMP based on a novel abstract data structure, which we call \textit{MathOptInterface}, for representing instances of mathematical optimization problems. MathOptInterface is significantly more general than existing data structures in the literature, encompassing, for example, a … Read more