In entry-exit gas markets as they are currently implemented in Europe, network constraints do not affect market interaction beyond the technical capacities determined by the TSO that restrict the quantities individual firms can trade at the market. It is an up to now unanswered question to what extent existing network capacity remains unused in an … Read more
Unit commitment (UC) is a key operational problem in power systems used to determine an optimal daily or weekly generation commitment schedule. Incorporating uncertainty in this already difficult mixed integer optimization problem introduces significant computational challenges. Most existing stochastic UC models consider either a two-stage decision structure, where the commitment schedule for the entire planning … Read more
We consider primal-dual IP methods where the linear system arising at each iteration is formulated in the reduced (augmented) form and solved approximately. Focusing on the iterates close to a solution, we analyze the accuracy of the so-called inexact step, i.e., the step that solves the unreduced system, when combining the effects of both different … Read more
Interior point methods (IPM) are the most popular approaches to solve Second Order Cone Optimization (SOCO) problems, due to their theoretical polynomial complexity and practical performance. In this paper, we present a warm-start method for primal-dual IPMs to reduce the number of IPM steps needed to solve SOCO problems that appear in a Branch and … Read more
In this paper, we extend the improved pointwise iteration-complexity result of a dynamic regularized alternating direction method of multipliers (ADMM) for a new stepsize domain. In this complexity analysis, the stepsize parameter can even be chosen in the interval $(0,2)$ instead of interval $(0,(1+\sqrt{5})/2)$. As usual, our analysis is established by interpreting this ADMM variant … Read more
In this study, we consider the special case of the uncapacitated p-hub center problem, where the weight/flow matrix includes 0 entities. In some real life networks, such as airline networks, cargo networks etc., the zero flow might exist between certain demand points. Typically in airline networks, nobody travels from city i to city i. In … Read more
Due to update the Lagrangian multiplier twice at each iteration, the symmetric alternating direction method of multipliers (S-ADMM) often performs better than other ADMM-type methods. In practice, some proximal terms with positive definite proximal matrices are often added to its subproblems, and it is commonly known that large proximal parameter of the proximal term often … Read more
This paper introduces a derivative-free and ready-to-use solver for nonlinear programs with nonlinear equality and inequality constraints (NLPs). Using finite differences and a sequential quadratic programming (SQP) approach, the algorithm aims at finding a local minimizer and no extra attempt is made to generate a globally optimal solution. Due to the use of finite differences, … Read more
We propose a gradient-based method for quadratic programming problems with a single linear constraint and bounds on the variables. Inspired by the GPCG algorithm for bound-constrained convex quadratic programming [J.J. More’ and G. Toraldo, SIAM J. Optim. 1, 1991], our approach alternates between two phases until convergence: an identification phase, which performs gradient projection iterations … Read more
In this article, we provide an overview of the current state of the art with respect to solution of mixed integer linear optimization problems (MILPS) in parallel. Sequential algorithms for solving MILPs have improved substantially in the last two decades and commercial MILP solvers are now considered effective off-the-shelf tools for optimization. Although concerted development … Read more