Dieter Weninger – Page 2 – Optimization Online

An Exact Projection-Based Algorithm for Bilevel Mixed-Integer Problems with Nonlinearities

Published: 2020/12/11, Updated: 2022/07/04

(Mixed) Integer Nonlinear Programming, Game Theory, Global Optimization bilevel optimization, global optimization, mixed-integer nonlinear programming, projection, strong duality

We propose an exact global solution method for bilevel mixed-integer optimization problems with lower-level integer variables and including nonlinear terms such as, \eg, products of upper-level and lower-level variables. Problems of this type are extremely challenging as a single-level reformulation suitable for off-the-shelf solvers is not available in general. In order to solve these problems … Read more

Time-Domain Decomposition for Optimal Control Problems Governed by Semilinear Hyperbolic Systems

Published: 2020/11/29, Updated: 2021/07/22

Systems governed by Differential Equations Optimization a posteriori error estimates, convergence analysis, optimal control, semilinear hyperbolic systems, time-domain decomposition

In this article, we extend the time-domain decomposition method described by Lagnese and Leugering (2003) to semilinear optimal control problems for hyperbolic balance laws with spatio-temporal varying coefficients. We provide the design of the iterative method applied to the global first-order optimality system, prove its convergence, and derive an a posteriori error estimate. The analysis … Read more

The SCIP Optimization Suite 7.0

Published: 2020/03/30

Matthias Miltenberger

(Mixed) Integer Linear Programming, (Mixed) Integer Nonlinear Programming benders decomposition, branch-and-cut, branch-and-price, column generation, constraint integer programming, linear programming, mixed-integer linear programming, mixed-integer nonlinear programming, mixed-integer semidefinite programming, optimization solver, parallelization, presolving, steiner tree optimization, tree size estimation

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 7.0 of the SCIP Optimization Suite. The new version features the parallel presolving library PaPILO as a new addition to the suite. PaPILO 1.0 simplifies … Read more

Two-row and two-column mixed-integer presolve using hash-based pairing methods

Published: 2019/09/03, Updated: 2020/07/08

(Mixed) Integer Linear Programming, Optimization Software Benchmark, Polyhedra linear programming, mixed-integer linear programming, optimization solver, presolve

In state-of-the-art mixed-integer programming solvers, a large array of reduction techniques are applied to simplify the problem and strengthen the model formulation before starting the actual branch-and-cut phase. Despite their mathematical simplicity, these methods can have significant impact on the solvability of a given problem. However, a crucial property for employing presolving techniques successfully is … Read more

A Decomposition Heuristic for Mixed-Integer Supply Chain Problems

Published: 2019/03/12, Updated: 2020/02/18

Lars Schewe

Martin Schmidt

Dieter Weninger

(Mixed) Integer Linear Programming, Supply Chain Management alternating direction method, decomposition, mixed-integer programming, penalty method, supply chain

Mixed-integer supply chain models typically are very large but are also very sparse and can be decomposed into loosely coupled blocks. In this paper, we use general-purpose techniques to obtain a block decomposition of supply chain instances and apply a tailored penalty alternating direction method, which exploits the structural properties of the decomposed instances. We … Read more

The SCIP Optimization Suite 5.0

Published: 2017/12/21, Updated: 2017/12/29

Matthias Miltenberger

(Mixed) Integer Linear Programming, (Mixed) Integer Nonlinear Programming branch-and-cut, branch-and-price, column generation framework, constraint integer programming, linear programming, mixed-integer linear programming, mixed-integer nonlinear programming, mixed-integer semidefinite programming, optimization solver, parallelization, steiner tree optimization

This article describes new features and enhanced algorithms made available in version 5.0 of the SCIP Optimization Suite. In its central component, the constraint integer programming solver SCIP, remarkable performance improvements have been achieved for solving mixed-integer linear and nonlinear programs. On MIPs, SCIP 5.0 is about 41 % faster than SCIP 4.0 and over … Read more

The SCIP Optimization Suite 4.0

Published: 2017/03/09, Updated: 2017/09/04

Matthias Miltenberger

(Mixed) Integer Nonlinear Programming, Optimization Software and Modeling Systems linear programming, mixed-integer linear and nonlinear programming, optimization solver development

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

Tackling Industrial-Scale Supply Chain Problems by Mixed-Integer Programming

Published: 2016/11/24

Gerald Gamrath

Ambros Gleixner

Thorsten Koch

Matthias Miltenberger

(Mixed) Integer Linear Programming, Supply Chain Management large-scale optimization, mixed-integer linear programming, numerical stability, primal heuristics, supply chain management, supply network optimization

SAP’s decision support systems for optimized supply network planning rely on mixed-integer programming as the core engine to compute optimal or near-optimal solutions. The modeling flexibility and the optimality guarantees provided by mixed-integer programming greatly aid the design of a robust and future-proof decision support system for a large and diverse customer base. In this … Read more

The SCIP Optimization Suite 3.2

Published: 2016/03/09

Matthias Miltenberger

Integer Programming, Linear, Cone and Semidefinite Programming, Optimization Software and Modeling Systems

The SCIP Optimization Suite is a software toolbox for generating and solving various classes of mathematical optimization problems. Its major components are the modeling language ZIMPL, the linear programming solver SoPlex, the constraint integer programming framework and mixed-integer linear and nonlinear programming solver SCIP, the UG framework for parallelization of branch-and-bound-based solvers, and the generic … Read more