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A Modified Simplex Method for Solving 1‐Norm Minimization Problem in Model Predictive Control
Author(s) -
Gupta Yash P.
Publication year - 2007
Publication title -
the canadian journal of chemical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.404
H-Index - 67
eISSN - 1939-019X
pISSN - 0008-4034
DOI - 10.1002/cjce.5450850208
Subject(s) - polyhedron , simplex , minification , mathematical optimization , norm (philosophy) , simplex algorithm , computer science , domain (mathematical analysis) , model predictive control , simple (philosophy) , computational complexity theory , mathematics , linear programming , algorithm , control (management) , artificial intelligence , combinatorics , mathematical analysis , philosophy , epistemology , political science , law
Since the simplex method requires the polyhedron to be in the positive domain, the 1‐norm minimization problems are formulated by substantially increasing the size of the LP problems. This paper presents a simple modification that enables the simplex method to be directly applicable to a polyhedron, which extends into the negative domain. That is, instead of requiring the problem to change, the method is changed to fit the problem. The modification eliminates the need to increase the size of the problem and thus eliminates the associated computational effort. The proposed method skips iterations and Phase 1 of the simplex method. Its computational advantage is verified in two examples.