Abstract. Home-Away Assignment problems are naturally cast as quadratic programming models in binary variables. In this work we compare alternative formulations. First, we propose another formulation by manipulating their special structure to obtain versions with 1/4 of the original size. By linearizing the quadratic objective function, we get two more alternative models to be compared with the quadratic ones. Numerical experiments exhibit the characteristics of each model. Palavras-chave.Sport scheduling, HA-assignment, Integer linear programming, Integer quadratic programming.

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DCISolver.jl is a new Julia (Bezanson et al., 2017) implementation of the Dynamic Control of Infeasibility method (DCI), introduced by Bielschowsky & Gomes ( 2008), for solving the equality-constrained nonlinear optimization problem minimizewhere f : R n → R and h : R n → R m are twice continuously differentiable. DCI is an iterative method that aims to compute a local minimum of (1) using first and second-order derivatives.Our initial motivation for developing DCISolver.jl is to solve PDE-constrained optimization problems, many of which have equality constraints only.

A very important area of research in the field of Mathematical Optimization is the benchmarking of optimization packages to compare solvers. During benchmarking, one usually collects a large amount of information like CPU time, number of functions evaluations, number of iterations, and much more. This information, if presented as tables, can be difficult to analyze and compare due to large amount of data. Therefore tools to better process and understand optimization benchmark data have been developed. One of the most widespread tools is the Performance Profile graphics proposed by Dolan and Moré [2]. In this context, this paper describes perprof-py, a free/open source software that creates Performance Profile graphics. This software produces graphics in PDF using LaTeX with PGF/TikZ [22] and PGFPLOTS [4] packages, in PNG using matplotlib [9], and in HTML using Bokeh [1]. Perprof-py can also be easily extended to be used with other plot libraries. It is implemented in Python 3 with support for internationalization, and is under the General Public License Version 3 (GPLv3).