Geometric Algorithm for Multiparametric Linear Programming

By Francesco Borrelli, Alberto Bemporad, Manfred Morari. 2003

233 citations recorded by the source corpus.

Subfields: Aerospace Engineering, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/dbadac48cd5bd3e4b8f299646d7baa3d578a9857

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Aerospace Engineering

1. Petter Tøndel
2. T. A. Johansen
3. J. Demmel
4. Grace Dinh
5. Francesco Borrelli
6. Alberto Bemporad
7. Eric C. Kerrigan
8. Colin Neil Jones

In Computational Theory and Mathematics

1. Francesco Borrelli
2. T. A. Johansen
3. Petter Tøndel
4. Grace Dinh
5. J. Demmel
6. Alberto Bemporad
7. Colin Neil Jones
8. Eric C. Kerrigan

In Numerical Analysis

1. Alberto Bemporad
2. Francesco Borrelli
3. T. A. Johansen
4. Petter Tøndel
5. J. Demmel
6. Grace Dinh
7. Eric C. Kerrigan
8. Anders Rantzer

Citations in the corpus

• Technical communique: On the facet-to-facet property of solutions to convex parametric quadratic programs (2006, methodology): “Several algorithms for solving a convex parametric quadratic program (pQP) (Baoti´ c, 2002; Bemporad et al., 2002b; Seron et al., 2003; Tondel et al., 2003a; Tondel et al., 2003b) and a parametric linear program (pLP) ( Borrelli et al., 2003 ) have recently been developed.”
• Communication-Optimal Convolutional Neural Nets (2018, methodology): “etermining a closed-form solution to the parameterized linear programs have been studied extensively in the context of control theory [GN72, BBM03, STJ05, JBM07]. We used the geometric algorithm from [BBM03], which we briefly describe in this section and fully specify in Figure 1.; see the original p”
• Relaxing dynamic programming (2006, background): “The solution can either be found by solving a multiparametric linear programming (MPLP) problem (see, e.g., [ 7 ]), or by doing explicit enumeration of the dual extreme points as is shown later.”
• Constrained Optimal Control of Linear and Hybrid Systems (2003, methodology): “The mp-LP solvers [68, 37] can detect critical regions of degeneracy and partition them into sub-regions where a unique optimum is defined.”
• An algorithm for multi-parametric quadratic programming and explicit MPC solutions (2001, methodology): “Multiparametric LP (mp-LP) is treated in (Gal, 1995) and ( Borrelli et al., 2000 ), mp-LP in connection with MPC based on linear programming is investigated in (Bemporad et al., accepted for publication), and multi-parametric mixed-integer linear programming (Dua and Pistikopoulos, to appear) is use”