A successive linear approximation algorithm for the global minimization of a concave quadratic program

In this work, we propose an algorithm for finding an approximate global minimum of a concave quadratic function with a negative semi-definite matrix, subject to linear equality and inequality constraints, where the variables are bounded with finite or infinite bounds. The proposed algorithm starts w...

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Vydáno v:Computational & applied mathematics Ročník 39; číslo 4
Hlavní autoři: Telli, Mohamed, Bentobache, Mohand, Mokhtari, Abdelkader
Médium: Journal Article
Jazyk:angličtina
Vydáno: Cham Springer International Publishing 01.12.2020
Springer Nature B.V
Témata:
Algorithms
Applications of Mathematics
Applied physics
Approximation
Computational mathematics
Computational Mathematics and Numerical Analysis
Linear programming
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
Matrix methods
Quadratic equations
90C20
Global optimization
Concave quadratic programming
Level curve
Linear programming
90C26
90C59
Numerical experiments
Approximation sets
ISSN:2238-3603, 1807-0302
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Shrnutí:In this work, we propose an algorithm for finding an approximate global minimum of a concave quadratic function with a negative semi-definite matrix, subject to linear equality and inequality constraints, where the variables are bounded with finite or infinite bounds. The proposed algorithm starts with an initial extreme point, then it moves from the current extreme point to a new one with a better objective function value. The passage from one basic feasible solution to a new one is done by the construction of certain approximation sets and solving a sequence of linear programming problems. In order to compare our algorithm with the existing approaches, we have developed an implementation with MATLAB and conducted numerical experiments on numerous collections of test problems. The obtained numerical results show the accuracy and the efficiency of our approach.
Bibliografie:ObjectType-Article-1
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ISSN:2238-3603
1807-0302
DOI:10.1007/s40314-020-01317-1