Support solving method for box-constrained indefinite quadratic minimisation problems
by Amar Andjouh; Mohand Ouamer Bibi
International Journal of Mathematical Modelling and Numerical Optimisation (IJMMNO), Vol. 12, No. 4, 2022

Abstract: This paper provides a new support solving method (SSM) of global optimisation for the box-constrained non-convex quadratic minimisation problem, in particular with one negative eigenvalue. We investigate the support of the objective function and exploit properties of the indefinite associated matrix for establishing global optimality criterion (necessary and sufficient conditions). Furthermore, using these conditions and computational techniques of abstract convexity, we suggest an SSM that can effectively solve an indefinite quadratic minimisation problem, providing thus a global minimiser. We present numerical examples and generate some test problems with known global minimiser, solving them by the proposed SSM. Finally, we provide the comparative effectiveness of the SSM with active set method (ASM) and interior point method (IPM) implemented under MATLAB optimisation toolbox.

Online publication date: Fri, 28-Oct-2022

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