This paper addresses the problem of generating synthetic test cases for experimentation in linear programming. We propose a method which maps instance generation and instance space search to an alternative encoded space. This allows us to develop a generator for feasible bounded linear programming instances with controllable properties. We show that this method is capable … Read more
Recently, parallel computing environments have become significantly popular. In order to obtain the benefit of using parallel computing environments, we have to deploy our programs for these effectively. This paper focuses on a parallelization of SCIP (Solving Constraint Integer Programs), which is a MIP solver and constraint integer programming framework available in source code. There … Read more
The proximal ADMM which adds proximal regularizations to ADMM’s subproblems is a popular and useful method for linearly constrained separable convex problems, especially its linearized case. A well-known requirement on guaranteeing the convergence of the method in the literature is that the proximal regularization must be positive semidefinite. Recently it was shown by He et … Read more
Several emerging applications, such as “Analytics of Things” and “Integrative Analytics” call for a fusion of statistical learning (SL) and stochastic optimization (SO). The Learning Enabled Optimization paradigm fuses concepts from these disciplines in a manner which not only enriches both SL and SO, but also provides a framework which supports rapid model updates and … Read more
The SCIP Optimization Suite is a powerful collection of optimization software that consists of the branch-cut-and-price framework and mixed-integer programming solver SCIP, the linear programming solver SoPlex, the modeling language Zimpl, the parallelization framework UG, and the generic branch-cut-and-price solver GCG. Additionally, it features the extensions SCIP-Jack for solving Steiner tree problems, PolySCIP for solving … Read more
We propose a novel asynchronous parallel algorithmic framework for the minimization of the sum of a smooth nonconvex function and a convex nonsmooth regularizer, subject to both convex and nonconvex constraints. The proposed framework hinges on successive convex approximation techniques and a novel probabilistic model that captures key elements of modern computational architectures and asynchronous … Read more
We present complexity and numerical results for a new asynchronous parallel algorithmic method for the minimization of the sum of a smooth nonconvex function and a convex nonsmooth regularizer, subject to both convex and nonconvex constraints. The proposed method hinges on successive convex approximation techniques and a novel probabilistic model that captures key elements of … Read more
Recent years have witnessed the surge of asynchronous parallel (async-parallel) iterative algorithms due to problems involving very large-scale data and a large number of decision variables. Because of asynchrony, the iterates are computed with outdated information, and the age of the outdated information, which we call \emph{delay}, is the number of times it has been … Read more
This paper describes a unified approach for solving Box-Constrained Optimization Problems (BCOP) in Euclidian spaces. The variables may be either continuous or discrete; in which case, they range on a grid of isolated points regularly spaced. For the continuous case, convergence is shown under standard assumptions; for the discrete case, slight modifications ensure that the … Read more
We contribute improvements to a Lagrangian dual solution approach applied to large-scale optimization problems whose objective functions are convex, continuously differentiable and possibly nonlinear, while the non-relaxed constraint set is compact but not necessarily convex. Such problems arise, for example, in the split-variable deterministic reformulation of stochastic mixed-integer optimization problems. The dual solution approach needs … Read more