Globally minimizing quadratic forms on Eucliean balls and spheres by algorithms for D.C. (difference of convex functions) optimization
We present new algorithm of d.c. optimization (DCA) for globally minimizing a (convex or nonconvex) quadratic form on an Euclidean ball or sphere: min{l_brace}{1/2}x{sup T} A x + b{sup T}x : {parallel}x{parallel} {<=} r{r_brace} (Q1) min{l_brace}{1/2}x{sup T} Ax + b{sup T}x : {parallel}x{parallel} = r{r_brace} (Q2) where A is n {times} n real symmetrix matrix, b {element_of} IR{sup n}, r is a positive number. DCA is attractive because it is computationally inexpensive and quite reliable. For a {open_quotes}good{close_quotes} d.c. decomposition of the objective function, we propose a simple DCA to solve (Q1). This algorithm can be also applied to solving (Q2). Numerical simulations on a series of test problems are reported. They show robustness, stability and superiority of DCA with respect to known standard methods in the literature. The use of DCA in Trust Region methods, in Constrained Eigenvalue problem and in Least Squares with Quadratic constraints is consequently very interesting.
- OSTI ID:
- 35764
- Report Number(s):
- CONF-9408161--
- Country of Publication:
- United States
- Language:
- English
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