By Yurii Nesterov, Arkadii Nemirovskii
Written for experts operating in optimization, mathematical programming, or keep an eye on conception. the overall idea of path-following and capability aid inside aspect polynomial time tools, inside aspect tools, inside aspect tools for linear and quadratic programming, polynomial time tools for nonlinear convex programming, effective computation equipment for regulate difficulties and variational inequalities, and acceleration of path-following equipment are lined. during this ebook, the authors describe the 1st unified concept of polynomial-time interior-point equipment. Their process offers a easy and stylish framework within which all recognized polynomial-time interior-point equipment could be defined and analyzed; this method yields polynomial-time interior-point equipment for a wide selection of difficulties past the normal linear and quadratic courses.
The booklet includes new and critical ends up in the overall idea of convex programming, e.g., their "conic" challenge formula in which duality thought is totally symmetric. for every set of rules defined, the authors conscientiously derive distinct bounds at the computational attempt required to unravel a given kin of difficulties to a given precision. in numerous instances they receive larger challenge complexity estimates than have been formerly recognized. a number of of the recent algorithms defined during this publication, e.g., the projective process, have been carried out, validated on "real international" difficulties, and located to be tremendous effective in perform.
Special positive factors o the constructed idea of polynomial tools covers all methods identified to date o provides specified descriptions of algorithms for lots of vital periods of nonlinear difficulties
Audience experts operating within the parts of optimization, mathematical programming, or regulate conception will locate this ebook priceless for learning interior-point equipment for linear and quadratic programming, polynomial-time equipment for nonlinear convex programming, and effective computational tools for keep an eye on difficulties and variational inequalities. A heritage in linear algebra and mathematical programming is important to appreciate the ebook. The distinct proofs and shortage of "numerical examples" may recommend that the ebook is of constrained price to the reader drawn to the sensible features of convex optimization, yet not anything can be farther from the reality. a whole bankruptcy is dedicated to capability aid tools accurately as a result of their nice potency in perform.
Contents bankruptcy 1: Self-Concordant capabilities and Newton strategy; bankruptcy 2: Path-Following Interior-Point equipment; bankruptcy three: power relief Interior-Point tools; bankruptcy four: how you can build Self-Concordant limitations; bankruptcy five: purposes in Convex Optimization; bankruptcy 6: Variational Inequalities with Monotone Operators; bankruptcy 7: Acceleration for Linear and Linearly restricted Quadratic difficulties; Bibliography; Appendix 1; Appendix 2.