Convergence rate of an optimization algorithm for minimizing quadratic functions with separable convex constraints. (English) Zbl 1168.65028

Kučera, Radek

SIAM J. Optim. 19, No. 2, 846-862 (2008).

The author studies a quadratic minimization problem with separable convex constraints. He begins by two sections which outline the studied problem, the necessary notation and background theorems, before proceeding to the description of the main algorithm (sections 3 and 4). The algorithm consists of a combination of the conjugate and projected gradient methods. Several theorems relating to the projected gradient and the particular implementation of the algorithm are proved. The fifth section studies the convergence properties of the algorithm and the sixth section gives details of the computational implementation. The paper concludes with a presentation of the computational results of the numerical tests performed by the author, and a list of relevant references.

Reviewer: Efstratios Rappos (Athens)

MSC:

65K05	Numerical mathematical programming methods
90C25	Convex programming
90C20	Quadratic programming

Keywords:

quadratic function; separable convex constraints; active set; conjugate gradient method; projected gradient; convergence; numerical examples; algorithm