Non-convex minimization of a quadratic function on a sphere

E. A. Kotel'nikov

Institute of Computational Mathematics and Mathematical Geophysics SB RAS, 6 Lavrentiev pr., Novosibirsk, 630090, Russia

Abstract: The minimization of convex functions on a sphere reduces to a sequence of problems minimizing its convex majorants on a sphere. To build majorants, the representation of the target function as a difference of convex quadratic functions and the solutions of the problem at the previous step is used. Representation of the target function in the form of a difference of convex quadratic functions is based on a modified procedure of decomposition of the Cholesky symmetric alternating-sign matrices.

Key words: quadratic optimization on sphere, collinearity gradients, convex majorant, Cholesky decomposition.

UDC: 519.853.32

Received: 23.06.2014
Revised: 25.07.2014

DOI: 10.15372/SJNM20150205

 English version: Numerical Analysis and Applications, 2015, 8:2, 135–147

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