Interior-Point Polynomial Algorithms in Convex Programming by Yurii Nesterov, Arkadii Nemirovskii

By Yurii Nesterov, Arkadii Nemirovskii

Written for experts operating in optimization, mathematical programming, or keep an eye on conception. the final thought of path-following and capability relief inside element polynomial time equipment, inside element equipment, inside aspect tools for linear and quadratic programming, polynomial time equipment for nonlinear convex programming, effective computation tools for regulate difficulties and variational inequalities, and acceleration of path-following equipment are lined. during this publication, the authors describe the 1st unified thought of polynomial-time interior-point tools. Their process offers a basic and stylish framework within which all recognized polynomial-time interior-point tools should be defined and analyzed; this strategy yields polynomial-time interior-point equipment for a wide selection of difficulties past the conventional 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 conception is totally symmetric. for every set of rules defined, the authors rigorously derive distinctive bounds at the computational attempt required to resolve a given family members of difficulties to a given precision. in different situations they receive greater challenge complexity estimates than have been formerly identified. numerous of the hot algorithms defined during this booklet, e.g., the projective strategy, have been applied, confirmed on "real global" difficulties, and located to be tremendous effective in perform.

Special gains o the constructed concept of polynomial equipment covers all methods identified to date o offers specified descriptions of algorithms for plenty of very important sessions of nonlinear difficulties

Audience experts operating within the components of optimization, mathematical programming, or regulate conception will locate this publication helpful for learning interior-point equipment for linear and quadratic programming, polynomial-time tools for nonlinear convex programming, and effective computational tools for keep watch over difficulties and variational inequalities. A historical past in linear algebra and mathematical programming is critical to appreciate the e-book. The particular proofs and absence of "numerical examples" may perhaps recommend that the publication is of restricted worth to the reader drawn to the sensible points of convex optimization, yet not anything can be farther from the reality. a complete bankruptcy is dedicated to power relief equipment accurately due to their nice potency in perform.

Contents bankruptcy 1: Self-Concordant capabilities and Newton technique; bankruptcy 2: Path-Following Interior-Point equipment; bankruptcy three: capability aid Interior-Point tools; bankruptcy four: how one can build Self-Concordant boundaries; 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.