In this letter, we present an alternative mixed-integer non-liner programming formulation of the reactive optimal power flow (ROPF) problem. We utilize a mixed-integer second-order cone programming (MISOCP) based approach to find global optimal solutions of the proposed ROPF problem formulation. We strengthen the MISOCP relaxation via the addition of convex envelopes and cutting planes. Computational … Read more
Distributionally robust optimization (DRO) has arose as an important paradigm to address the issue of distributional ambiguity in decision optimization. In its standard form, DRO seeks an optimal solution against the worst-possible expected value evaluated based on a set of candidate distributions. In the case where a decision maker is not risk neutral, the most … Read more
Several authors have studied the problem of making an asymmetric cone symmetric through a change of inner product, and one set of positive results pertains to the class of elliptic cones. We demonstrate that the class of elliptic cones is equal to the class of induced-norm cones that arise through Jordan-isomorphism with the second-order cone, … Read more
The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. This paper discusses enhancements and extensions contained in version 7.0 of the SCIP Optimization Suite. The new version features the parallel presolving library PaPILO as a new addition to the suite. PaPILO 1.0 simplifies … Read more
The symmetric alternating direction method of multipliers (S-ADMM) is a classical effective method for solving two-block separable convex optimization. However, its convergence may not be guaranteed for multi-block case providing there is no additional assumptions. In this paper, we propose a partial PPa S-ADMM (referred as P3SADMM), which updates the Lagrange multiplier twice with suitable … Read more
We propose a dynamic version of the classical node packing problem, also called the stable set or independent set problem. The problem is defined by a node set, a node weight vector, and an edge probability vector. For every pair of nodes, an edge is present or not according to an independent Bernoulli random variable … Read more
We consider exact deterministic mixed-integer programming (MIP) reformulations of distributionally robust chance-constrained programs (DR-CCP) with random right-hand sides over Wasserstein ambiguity sets. The existing MIP formulations are known to have weak continuous relaxation bounds, and, consequently, for hard instances with small radius, or with a large number of scenarios, the branch-and-bound based solution processes suffer … Read more
We present a new variant of the Chambolle–Pock primal–dual method with Bregman distances, analyze its convergence, and apply it to the centering problem in sparse semidefinite programming. The novelty in the method is a line search procedure for selecting suitable step sizes. The line search obviates the need for estimating the norm of the constraint … Read more
Augmented Lagrangian algorithms are very popular and successful methods for solving constrained optimization problems. Recently, the global convergence analysis of these methods have been dramatically improved by using the notion of the sequential optimality conditions. Such conditions are optimality conditions independently of the fulfilment of any constraint qualifications and provide theoretical tools to justify stopping … Read more
While transmission switching is known to reduce power generation costs, the difficulty of solving even DC optimal transmission switching (DCOTS) has prevented optimal transmission switching from becoming commonplace in real-time power systems operation. In this paper, we present a k-nearest neighbors (KNN) heuristic for DCOTS which relies on the insight that, for routine operations on … Read more