Geodesic
Non-convex minimization of a~quadratic function on a~sphere
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 18 (2015) no. 2, pp. 163-176

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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. 
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     author = {E. A. Kotel'nikov},
     title = {Non-convex minimization of a~quadratic function on a~sphere},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {163--176},
     publisher = {mathdoc},
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     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2015_18_2_a4/}
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E. A. Kotel'nikov. Non-convex minimization of a~quadratic function on a~sphere. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 18 (2015) no. 2, pp. 163-176. http://geodesic.mathdoc.fr/item/SJVM_2015_18_2_a4/