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 methods that approximate 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 computation time for solving linear programming problems, we propose two arc-search interior-point methods using Nesterov’s restarting … Read more

Orbital Crossover

Symmetry in optimization has been known to wreak havoc in optimization algorithms. Often, some of the hardest instances are highly symmetric. This is not the case in linear programming, as symmetry allows one to reduce the size of the problem, possibly dramatically, while still maintaining the same optimal objective value. This is done by aggregating … Read more

General Polyhedral Approximation of Two-Stage Robust Linear Programming

\(\) We consider two-stage robust linear programs with a budget of uncertainty for the righthand side. In this scenario set, which is frequently used in robust optimization, the uncertain righthand side for each row lies in an interval and the relative increases summed over all rows are less than a budget \(\Gamma\). We develop a … Read more

A primal-dual majorization-minimization method for large-scale linear programs

We present a primal-dual majorization-minimization method for solving large-scale linear programs. A smooth barrier augmented Lagrangian (SBAL) function with strict convexity for the dual linear program is derived. The majorization-minimization approach is naturally introduced to develop the smoothness and convexity of the SBAL function. Our method only depends on a factorization of the constant matrix … Read more

Tight Probability Bounds with Pairwise Independence

\(\) While useful probability bounds for \(n\) pairwise independent Bernoulli random variables adding up to at least an integer \(k\) have been proposed in the literature, none of these bounds are tight in general. In this paper, we provide several results in this direction. Firstly, when \(k = 1\), the tightest upper bound on the … Read more

On the Sparsity of Optimal Linear Decision Rules in Robust Inventory Management

We consider the widely-studied class of production-inventory problems from the seminal work of Ben-Tal et al. (2004) on linear decision rules in robust optimization. We prove that there always exists an optimal linear decision rule for this class of problems in which the number of nonzero parameters in the linear decision rule is equal to … Read more

Revisiting Degeneracy, Strict Feasibility, Stability, in Linear Programming

Currently, the simplex method and the interior point method are indisputably the most popular algorithms for solving linear programs, LPs. Unlike general conic programs, LPs with a finite optimal value do not require strict feasibility in order to establish strong duality. Hence strict feasibility is seldom a concern, even though strict feasibility is equivalent to … Read more

The SCIP Optimization Suite 8.0

The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. This paper discusses enhancements and extensions contained in version 8.0 of the SCIP Optimization Suite. Major updates in SCIP include improvements in symmetry handling and decomposition algorithms, new cutting planes, a new plugin type … Read more

A Robust Optimization Method with Successive Linear Programming for Intensity Modulated Radiation Therapy

Intensity modulated radiation therapy (IMRT) is one of radiation therapies for cancers, and it is considered to be effective for complicated shapes of tumors, since dose distributions from each irradiation can be modulated arbitrary. Fluence map optimization (FMO), which optimizes beam intensities with given beam angles, is often formulated as an optimization problem with dose … Read more