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Nonlinear optimization. Complexity issues. (English) Zbl 0785.90091
International Series of Monographs on Computer Science. 8. New York: Oxford University Press. xii, 165 p. (1991).
This book is based on notes for a one-semester graduate course.
The first two chapters give brief descriptions of optimization theory and complexity theory; and then some specific algorithms for convex and nonconvex quadratic programming and their complexities are discussed. This is also done in the final chapter for the black-box model, that is, one in which the objective function is defined in terms of a black-box which for each given input vector \(x\) there is an output \(f(x)\).
Chapter headings are: 1. Optimization and convexity; 2. Complexity theory; 3. Convex quadratic programming; 4. Nonconvex quadratic programming; 5. Local optimization; 6. Complexity in the black-box model.

MSC:
90C30 Nonlinear programming
90-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to operations research and mathematical programming
90C60 Abstract computational complexity for mathematical programming problems
90C05 Linear programming
90C20 Quadratic programming
90C26 Nonconvex programming, global optimization
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