We consider a problem involving a set of agents who need to coordinate their actions to optimize the sum of their objectives while satisfying a common resource constraint. The objective functions of the agents are unknown to them a priori and are revealed in an online manner. The resulting problem is an online optimization problem … Read more
A specialized algorithm for quadratic optimization (QO, or, formerly, QP) with disjoint linear constraints is presented. In the considered class of problems, a subset of variables are subject to linear equality constraints, while variables in a different subset are constrained to remain in a convex set. The proposed algorithm exploits the structure by combining steps … Read more
This paper presents an accelerated composite gradient (ACG) variant, referred to as the AC-ACG method, for solving nonconvex smooth composite minimization problems. As opposed to well-known ACG variants that are either based on a known Lipschitz gradient constant or a sequence of maximum observed curvatures, the current one is based on a sequence of average … Read more
Cutting planes from the Boolean Quadric Polytope (BQP) can be used to reduce the optimality gap of the NP-hard nonconvex quadratic program with box constraints (BoxQP). It is known that all cuts of the Chvátal-Gomory closure of the BQP are A-odd cycle inequalities. We obtain a compact extended relaxation of all A-odd cycle inequalities, which … Read more
In state-of-the-art mixed-integer programming solvers, a large array of reduction techniques are applied to simplify the problem and strengthen the model formulation before starting the actual branch-and-cut phase. Despite their mathematical simplicity, these methods can have significant impact on the solvability of a given problem. However, a crucial property for employing presolving techniques successfully is … Read more
Given the inability to foresee all possible scenarios, it is justified to desire an efficient trust-region subproblem solver capable of delivering any desired level of accuracy on demand; that is, the accuracy obtainable for a given trust-region subproblem should not be partially dependent on the problem itself. Current state-of-the-art iterative eigensolvers all fall into the … Read more
The superiorization methodology is intended to work with input data of constrained minimization problems, that is, a target function and a set of constraints. However, it is based on an antipodal way of thinking to what leads to constrained minimization methods. Instead of adapting unconstrained minimization algorithms to handling constraints, it adapts feasibility-seeking algorithms to … Read more
In this work, we consider a risk-averse ultimate pit problem where the grade of the mineral is uncertain. We propose a two-stage formulation of the problem and discuss which properties are desirable for a risk measure in this context. We show that the only risk measure that satisfies these properties is the entropic. We propose … Read more
Pivoting methods are of vital importance for linear programming, the simplex method being the by far most well-known. In this paper, a primal-dual pair of linear programs in canonical form is considered. We show that there exists a sequence of pivots, whose length is bounded by the minimum dimension of the constraint matrix, such that … Read more
Domain-Driven Solver (DDS) is a MATLAB-based software package for convex optimization problems in Domain-Driven form [11]. The current version of DDS accepts every combination of the following function/set constraints: (1) symmetric cones (LP, SOCP, and SDP); (2) quadratic constraints; (3) direct sums of an arbitrary collection of 2-dimensional convex sets defined as the epigraphs of … Read more