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
The scheduling of drilling and hydraulic fracturing of wells in an unconventional oil field plays an important role in the profitability of the field. A key challenge arising in this problem is the requirement that neither drilling nor oil production can be done at wells within a specified neighborhood of a well being fractured. We … Read more
This work considers nonsmooth and nonconvex optimization problems whose objective and constraint functions are defined by difference-of-convex (DC) functions. We consider an infeasible bundle method based on the so-called improvement functions to compute critical points for problems of this class. Our algorithm neither employs penalization techniques nor solves subproblems with linearized constraints. The approach, which … Read more
Quadratically constrained quadratic programs (QCQPs) are a fundamental class of optimization problems well-known to be NP-hard in general. In this paper we study sufficient conditions for a convex hull result that immediately implies that the standard semidefinite program (SDP) relaxation of a QCQP is tight. We begin by outlining a general framework for proving such … Read more
A hybrid projection-proximal point algorithm is proposed for variational inequality problems. Though the usual proximal point method and its variants require that the mapping involved be monotone, at least pseudomonotone, we assume only that the so-called Minty variational inequality has a solution, in order to ensure the global convergence. This assumption is less stringent than … Read more