Solving a linear program via a single unconstrained minimization

This paper proposes a novel approach for solving linear programs. We reformulate a primal-dual linear program as an unconstrained minimization of a convex and twice continuously differentiable merit function. When the optimal set of the primal-dual pair is nonempty, its optimal set is equal to the optimal set of the proposed merit function. Minimizing this … Read more

When Does Primal Interior Point Method Beat Primal-dual in Linear Optimization?

The primal-dual interior point method (IPM) is widely regarded as the most efficient IPM variant for linear optimization. In this paper, we demonstrate that the improved stability of the pure primal IPM can allow speedups relative to a primal-dual solver, particularly as the IPM approaches convergence.  The stability of the primal scaling matrix makes it … Read more

Immunity to Increasing Condition Numbers of Linear Superiorization versus Linear Programming

Given a family of linear constraints and a linear objective function one can consider whether to apply a Linear Programming (LP) algorithm or use a Linear Superiorization (LinSup) algorithm on this data. In the LP methodology one aims at finding a point that fulfills the constraints and has the minimal value of the objective function … Read more

A Primal-Dual Frank-Wolfe Algorithm for Linear Programming

We present two first-order primal-dual algorithms for solving saddle point formulations of linear programs, namely FWLP (Frank-Wolfe Linear Programming) and FWLP-P. The former iteratively applies the Frank-Wolfe algorithm to both the primal and dual of the saddle point formulation of a standard-form LP. The latter is a modification of FWLP in which regularizing perturbations are … Read more

The SCIP Optimization Suite 9.0

The SCIP Optimization Suite provides a collection of software packages for mathematical optimization, centered around the constraint integer programming (CIP) framework SCIP. This report discusses the enhancements and extensions included in the SCIP Optimization Suite 9.0. The updates in SCIP 9.0 include improved symmetry handling, additions and improvements of nonlinear handlers and primal heuristics, a … Read more

Distributionally robust optimization through the lens of submodularity

Distributionally robust optimization is used to solve decision making problems under adversarial uncertainty where the distribution of the uncertainty is itself ambiguous. In this paper, we identify a class of these instances that is solvable in polynomial time by viewing it through the lens of submodularity. We show that the sharpest upper bound on the … Read more

Combining Precision Boosting with LP Iterative Refinement for Exact Linear Optimization

This article studies a combination of the two state-of-the-art algorithms for the exact solution of linear programs (LPs) over the rational numbers, i.e., without any roundoff errors or numerical tolerances. By integrating the method of precision boosting inside an LP iterative refinement loop, the combined algorithm is able to leverage the strengths of both methods: … Read more

PaPILO: A Parallel Presolving Library for Integer and Linear Optimization with Multiprecision Support

Presolving has become an essential component of modern MIP solvers both in terms of computational performance and numerical robustness. In this paper we present PaPILO (https://github.com/scipopt/papilo), a new C++ header-only library that provides a large set of presolving routines for MIP and LP problems from the literature. The creation of \papilo was motivated by the … Read more

Application of a Gas Market Model with Linear Programming. The Influence of the Dollar Exchange Rate on the Wholesale Price of Natural Gas in Northwest Europe until 2040

The price of natural gas at wholesale markets in Northwest Europe is influenced by numerous parameters. The USD to EUR exchange rate is one of these parameters. Using the LP-based gas market model WEGA, this paper will examine the impact of USD exchange rates on wholesale natural gas prices in Northwest Europe from 2025 to … Read more

An infeasible interior-point arc-search method with Nesterov’s restarting strategy for linear programming problems

An arc-search interior-point method is a type of interior-point method that approximates the central path by an ellipsoidal arc, and it can often reduce the number of iterations. In this work, to further reduce the number of iterations and the computation time for solving linear programming problems, we propose two arc-search interior-point methods using Nesterov’s … Read more