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Quadratic optimization. (English) Zbl 0833.90091
Horst, Reiner et al., Handbook of global optimization. Dordrecht: Kluwer Academic Publishers. Nonconvex Optim. Appl. 2, 217-269 (1995).
Summary: Quadratic optimization comprises one of the most important areas of nonlinear programming. Numerous problems in real world applications, including problems in planning and scheduling, economies of scale, and engineering design, and control are naturally expressed as quadratic problems. Moreover, the quadratic problem is known to be NP-hard, which makes this one of the most interesting and challenging class of optimization problems. In this chapter, we review various properties of the quadratic problem, and discuss different techniques for solving various classes of quadratic problems. Some of the more successful algorithms for solving the special cases of bound constrained and large scale quadratic problems are considered. Examples of various applications of quadratic programming are presented. A summary of the available computational results for the algorithms to solve the various classes of problems is presented. For the entire collection see [Zbl 0805.00009].

MSC:
90C20Quadratic programming
90-02Research monographs (optimization)
90C06Large-scale problems (mathematical programming)