We propose a linear programming method that is based on active-set changes and proximal-point iterations. The method solves a sequence of least-distance problems using a warm-started quadratic programming solver that can reuse internal matrix factorizations from the previously solved least-distance problem. We show that the proposed method terminates in a finite number of iterations and that it outperforms state-of-the-art LP solvers in scenarios where an extensive number of small/medium scale LPs need to be solved rapidly, occurring in, for example, multi-parametric programming algorithms. In particular, we show how the proposed method can accelerate operations such as redundancy removal, computation of Chebyshev centers and solving linear feasibility problems.

A Linear Programming Method Based on Proximal-Point Iterations with Applications to Multi-Parametric Programming

Bemporad A.;
2022

Abstract

We propose a linear programming method that is based on active-set changes and proximal-point iterations. The method solves a sequence of least-distance problems using a warm-started quadratic programming solver that can reuse internal matrix factorizations from the previously solved least-distance problem. We show that the proposed method terminates in a finite number of iterations and that it outperforms state-of-the-art LP solvers in scenarios where an extensive number of small/medium scale LPs need to be solved rapidly, occurring in, for example, multi-parametric programming algorithms. In particular, we show how the proposed method can accelerate operations such as redundancy removal, computation of Chebyshev centers and solving linear feasibility problems.
Optimization algorithms
predictive control for linear systems
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11771/20179
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