ON ON AN EFFICIENT IMPLEMENTATION OF THE FACE ALGORITHM FOR LINEAR PROGRAMMING”
Zhang et al recently propose another approach to the face algorithm. This note gives a modification of the result. ArticleDownload View PDF
Month: April 2015
Strong SOCP Relaxations for the Optimal Power Flow Problem
This paper proposes three strong second order cone programming (SOCP) relaxations for the AC optimal power flow (OPF) problem. These three relaxations are incomparable to each other and two of them are incomparable to the standard SDP relaxation of OPF. Extensive computational experiments show that these relaxations have numerous advantages over existing convex relaxations in … Read more
Beam Search for integer multi-objective optimization
Beam search is a tree search procedure where, at each level of the tree, at most W nodes are kept. This results in a metaheuristic whose solving time is polynomial in W. Popular for single-objective problems, beam search has only received little attention in the context of multi-objective optimization. By introducing the concepts of oracle … Read more
K-Adaptability in Two-Stage Distributionally Robust Binary Programming
We propose to approximate two-stage distributionally robust programs with binary recourse decisions by their associated K-adaptability problems, which pre-select K candidate second-stage policies here-and-now and implement the best of these policies once the uncertain parameters have been observed. We analyze the approximation quality and the computational complexity of the K-adaptability problem, and we derive explicit … Read more
An O(1/k) Convergence Rate for the Variable Stepsize Bregman Operator Splitting Algorithm
An earlier paper proved the convergence of a variable stepsize Bregman operator splitting algorithm (BOSVS) for minimizing $\phi(Bu)+H(u)$ where $H$ and $\phi$ are convex functions, and $\phi$ is possibly nonsmooth. The algorithm was shown to be relatively efficient when applied to partially parallel magnetic resonance image reconstruction problems. In this paper, the convergence rate of … Read more
A proximal gradient method for ensemble density functional theory
The ensemble density functional theory is valuable for simulations of metallic systems due to the absence of a gap in the spectrum of the Hamiltonian matrices. Although the widely used self-consistent field iteration method can be extended to solve the minimization of the total energy functional with respect to orthogonality constraints, there is no theoretical … Read more
Some Applications of Polynomial Optimization in Operations Research and Real-Time Decision Making
We demonstrate applications of algebraic techniques that optimize and certify polynomial inequalities to problems of interest in the operations research and transportation engineering communities. Three problems are considered: (i) wireless coverage of targeted geographical regions with guaranteed signal quality and minimum transmission power, (ii) computing real-time certificates of collision avoidance for a simple model of … Read more
An exact solution method for binary equilibrium problems with compensation and the power market uplift problem
We propose a novel method to fi nd Nash equilibria in games with binary decision variables by including compensation payments and incentive-compatibility constraints from non-cooperative game theory directly into an optimization framework in lieu of using first order conditions of a linearization, or relaxation of integrality conditions. The reformulation off ers a new approach to obtain and … Read more
Decomposition algorithm for large-scale two-stage unit-commitment
Everyday, electricity generation companies submit a generation schedule to the grid operator for the coming day; computing an optimal schedule is called the unit-commitment problem. Generation companies can also occasionally submit changes to the schedule, that can be seen as intra-daily incomplete recourse actions. In this paper, we propose a two-stage formulation of unit-commitment, wherein … Read more
Quantum and classical coin-flipping protocols based on bit-commitment and their point games
We focus on a family of quantum coin-flipping protocols based on quantum bit-commitment. We discuss how the semidefinite programming formulations of cheating strategies can be reduced to optimizing a linear combination of fidelity functions over a polytope. These turn out to be much simpler semidefinite programs which can be modelled using second-order cone programming problems. … Read more