## A D. C. optimization algorithm for solving the trust-region subproblem.(English)Zbl 0913.65054

The authors consider the optimization problem $g(x)- h(x)\to \inf_{x\in\mathbb{R}^n},$ where the functions $$g$$ and $$h$$ are convex. For this d.c. optimization problem, the authors give duality, local and global optimization conditions and a numerical algorithm. The given algorithm is applied for the solution of a trust-region problem of the form ${1\over 2}\cdot x^T\cdot A\cdot x+ b^T\cdot x\to \inf_{\| x\|\leq r}.$ Numerical experiments are given and relations to the Goldstein-Levitin-Polyak gradient projection algorithm in the convex case are discussed.

### MSC:

 65K05 Numerical mathematical programming methods 90C26 Nonconvex programming, global optimization
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