We investigate how the numerical properties of the LP relaxations evolve throughout the solution procedure in a solver employing the branch-and-cut algorithm. The long-term goal of this work is to determine whether the effect on the numerical conditioning of the LP relaxations resulting from the branching and cutting operations can be effectively predicted and whether … Read more
We propose a communication- and computation-efficient distributed optimization algorithm using second-order information for solving ERM problems with a nonsmooth regularization term. Current second-order and quasi-Newton methods for this problem either do not work well in the distributed setting or work only for specific regularizers. Our algorithm uses successive quadratic approximations, and we describe how to … Read more
In this paper, we develop a new algorithmic framework that handles black box problems with integer variables. The strategy included in the framework makes use of specific search directions (so called primitive directions) and a suitably developed nonmonotone line search, thus guaranteeing a high level of freedom when exploring the integer lattice. We first describe … Read more
The demand for model-based simulation and optimization solutions requires the availability of software frameworks that not only provide computational capabilities, but also help to ease the formulation and implementation of the respective optimal control problems. In this article, we present and discuss recent development efforts and applicable work flows using the example of MUSCOD, the … Read more
We present CasADi, an open-source software framework for numerical optimization. CasADi is a general-purpose tool that can be used to model and solve optimization problems with a large degree of flexibility, larger than what is associated with popular algebraic modeling languages such as AMPL, GAMS, JuMP or Pyomo. Of special interest are problems constrained by … Read more
In this paper we present SDDP.jl, an open-source library for solving multistage stochastic optimization problems using the Stochastic Dual Dynamic Programming algorithm. SDDP.jl is built upon JuMP, an algebraic modelling language in Julia. This enables a high-level interface for the user, while simultaneously providing performance that is similar to implementations in low-level languages. We benchmark … Read more
It is shown how to use the performance and data profile benchmarking tools to improve algorithms’ performance. An illustration for the BFO derivative-free optimizer suggests that the obtained gains are potentially significant. Citation ACM Transactions on Mathematical Software, 45:2 (2019), Article 20. Article Download View A note on using performance and data profiles for training … Read more
Distributed optimization algorithms are essential for training machine learning models on very large-scale datasets. However, they often suffer from communication bottlenecks. Confronting this issue, a communication-efficient primal-dual coordinate ascent framework (CoCoA) and its improved variant CoCoA+ have been proposed, achieving a convergence rate of $\mathcal{O}(1/t)$ for solving empirical risk minimization problems with Lipschitz continuous losses. … Read more
We describe BASBL, our implementation of the deterministic global optimization algorithm Branch-and-Sandwich for nonconvex/nonlinear bilevel problems, within the open-source MINOTAUR framework. The solver incorporates the original Branch-and-Sandwich algorithm and modifications proposed in the first part of this work. We also introduce BASBLib, an extensive online library of bilevel benchmark problems collected from the literature and … Read more
We present a flexible framework for general mixed-integer nonlinear programming (MINLP), called Minotaur, that enables both algorithm exploration and structure exploitation without compromising computational efficiency. This paper documents the concepts and classes in our framework and shows that our implementations of standard MINLP techniques are efficient compared with other state-of-the-art solvers. We then describe structure-exploiting … Read more