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An efficient algorithm for globally minimizing a quadratic function under convex quadratic constraints. (English) Zbl 0952.90031
The author gives two approaches to minimizing a quadratic function subject to strictly convex quadratic constraints which can be formulated as follows: $$\text{Minimize}\quad q_0(x)\quad\text{subjec to }\quad q_i(x)\le 0\qquad (i= 1,\dots,m),$$ $$\text{where}\quad q_i(x)= (A_ix,x)/2+ (b^i, x)- r_i.$$ The first approach is a d.c. optimization algorithm whose main tools are the proximal point algorithm and/or the projection subgradient method. The second approach is a branch-and-bound scheme using Lagrangian duality. -- Several numerical experiments are given.

90C20Quadratic programming
65K05Mathematical programming (numerical methods)
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