This paper aims to develop distributed algorithms for nonconvex optimization problems with complicated constraints associated with a network. The network can be a physical one, such as an electric power network, where the constraints are nonlinear power flow equations, or an abstract one that represents constraint couplings between decision variables of different agents. Despite the … Read more
Principal angles between linear subspaces have been studied for their application to statistics, numerical linear algebra, and other areas. In 2005, Iusem and Seeger defined critical angles within a single convex cone as an extension of antipodality in a compact set. Then, in 2016, Seeger and Sossa extended that notion to two cones. This was … Read more
We present a detailed set of performance comparisons of two state-of-the-art solvers for the application of designing time-delay compensators, an important problem in the field of robust control. Formulating such robust control mechanics as constrained optimization problems often involves objective and constraint functions that are both nonconvex and nonsmooth, both of which present significant challenges … Read more
We present a model development framework and numerical solution approach to the general problem-class of packing convex objects into optimized convex containers. Specifically, here we discuss the problem of packing ovals (egg-shaped objects, defined here as generalized ellipses) into optimized regular polygons in R”. Our solution strategy is based on the use of embedded Lagrange … Read more
LSP(n), the largest small polygon with n vertices, is defined as the polygon of unit diameter that has maximal area A(n). Finding the configuration LSP(n) and the corresponding A(n) for even values n >= 6 is a long-standing challenge that leads to an interesting class of nonlinear optimization problems. We present numerical solution estimates for … Read more
High school timetabling problems consist in building periodic timetables for class-teacher meetings considering compulsory and non-compulsory requisites. This family of problems has been widely studied since the 1950s, mostly via mixed-integer programming and metaheuristic techniques. However, the efficient obtention of optimal or near-optimal solutions is still a challenge for many problems of practical size. In … Read more
We present the PyMOSO software package for (1) solving multi-objective simulation optimization (MOSO) problems on integer lattices, and (2) implementing and testing new simulation optimization (SO) algorithms. First, for solving MOSO problems on integer lattices, PyMOSO implements R-PERLE, a state-of-the-art algorithm for two objectives, and R-MinRLE, a competitive benchmark algorithm for three or more objectives. … Read more
We present a scalable branching method for the dual decomposition of stochastic mixed-integer programming. Our new branching method is based on the branching method proposed by Caro e and Schultz that creates branching disjunctions on first-stage variables only. We propose improvements to the process for creating branching disjunctions, including 1) branching on the optimal solutions … Read more
In contrast with many other convex optimization classes, state-of-the-art semidefinite programming solvers are yet unable to efficiently solve large scale instances. This work aims to reduce this scalability gap by proposing a novel proximal algorithm for solving general semidefinite programming problems. The proposed methodology, based on the primal-dual hybrid gradient method, allows the presence of … Read more
We present POLO — a C++ library for large-scale parallel optimization research that emphasizes ease-of-use, flexibility and efficiency in algorithm design. It uses multiple inheritance and template programming to decompose algorithms into essential policies and facilitate code reuse. With its clear separation between algorithm and execution policies, it provides researchers with a simple and powerful … Read more