4 edition of **Self-concordant functions and polynomial-time methods in convex programming** found in the catalog.

Self-concordant functions and polynomial-time methods in convex programming

Nesterov, IНЎU. E.

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Published
**1989**
by USSR Academy of Sciences, Central Economic & Mathematic Institute in Moscow
.

Written in English

- Convex programming.

**Edition Notes**

Other titles | Samosoglasovannye funkt͡sii i polinominalʹnye algoritmy v vypuklom programmirovanii., Polynomial-time methods in convex programming. |

Statement | Ju.E. Nesterov, A.S. Nemirovsky. |

Series | Materialy po matematicheskomu obespechenii͡u ĖVM, Materialy po matematicheskomu obespechenii͡u ĖVM (Moscow, R.S.F.S.R.) |

Contributions | Nemirovskiĭ, Arkadiĭ Semenovich. |

Classifications | |
---|---|

LC Classifications | QA402.5 .N462 1989 |

The Physical Object | |

Pagination | 194 p. ; |

Number of Pages | 194 |

ID Numbers | |

Open Library | OL1904250M |

LC Control Number | 90106681 |

Specialists working in the areas of optimization, mathematical programming, or control theory will find this book invaluable for studying interior-point methods for linear and quadratic programming, polynomial-time methods for nonlinear convex programming, and efficient computational methods for control problems and variational inequalities. Actually, this was a major challenge. At the time only the theory of interior-point methods for linear optimization was polished enough to be explained to students. The general theory of self-concordant functions had appeared in print only once in the form of research monograph [12].Brand: Springer US.

It enabled solutions of linear programming problems that were beyond the capabilities of the simplex method. Contrary to the simplex method, it reaches a best solution by traversing the interior of the feasible region. The method can be generalized to convex programming based on a self-concordant barrier function used to encode the convex set. self-concordance-based theory of polynomial-time interior-point methods de-veloped in Nesterov and Nemirovski (); this theory explained the nature of existing interior-point methods (IPMs) for LP and allowed the extension of these methods to the entire ﬁeld of convex programming. We now provide an overview of the basic results of this.

The authors also discuss the complexity issues and provide an overview of the basic theory of state-of-the-art polynomial time interior point methods for linear, conic quadratic, and semidefinite programming. The book's focus on well-structured convex problems in conic form allows for unified theoretical and algorithmical treatment of a wide. in the case of convex optimization problems with special convex functions and block diagonal structure in the constraints [9]. However, this function is not a self-concordant barrier and to the best of our knowledge, the role of self-concordant barriers in this context was previously non-existent.

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State of the art. The self-concordance-based theory of interior point (IP) polynomial methods in Convex Programming [5] is commonly recognized as the standard approach to the design of theo-retically e cient IP methods for convex optimization programs.

A natural question is whether this. We demonstrate (§) that self-concordant functions form a nice field for the Newton method, which allows us to develop general theory of polynomial-time path-following algorithms (Chapter 3); as demonstrated by the general existence theorem (§), the related methods in principle can be used to solve an arbitrary convex problem.

Section is devoted to the Legendre transformation of self. Among other things, self-concordant functions are useful in the analysis of Newton's method. Self-concordant barrier functions are used to develop the barrier functions used in interior point methods for convex and nonlinear optimization.

Appendix F. Self-Concordant Barrier Functions for Convex Optimization that is self concordant on the set S = x: aT i x−b i ≥ 0,i=1,m. For the remainder of this Chapter, we make several assumptions to simplify our discussion. They are not essential; in fact, almost identicalresults can be proved without these Size: KB.

Written for specialists working in optimization, mathematical programming, or control theory. The general theory of path-following and potential reduction interior point polynomial time methods, interior point methods, interior point methods for linear and quadratic programming, polynomial time methods for nonlinear convex programming, efficient computation methods for control problems and.

The purpose of this book is to present the general theory of interior-point polynomial-time methods for convex programming. Since the publication of Karmarkar's famous paper inthe area has been intensively developed by many researchers, who have focused on linear and quadratic programming.

the notion of a self-concordant conv ex function – the basic ingredient of the self-concordance-based. theory of IP methods – to the case of convex-concav e functions Author: Arkadi Nemirovski. The algorithm is shown to be of global convergence and of polynomial-time complexity.

Keywords: Multi-stage stochastic nonlinear programming, Lagrangian dual, Self-concordant barrier, Interior Point Methods, Polynomial-time Complexity. The research is partially supported by Grant RP of National University of Singapore. This book provides a comprehensive, modern introduction to convex optimization, a field that is becoming increasingly important in applied mathematics, economics and finance, engineering, and computer science, notably in data science and machine learning.

Self-Concordant Functions: Newton Method Analysis • Consider Newton’s method, started at x0, with backtracking line search. • Assume that f: Rn → R is self-concordant and strictly convex. (If domf 6= Rn, assume the level set {x | f(x) ≤ f(x0)} is closed.

• Also, assume that f is bounded from Size: KB. Separable self-concordant spectral functions and a conjecture of Tunçel Article in Mathematical Programming (1) September with 4 Reads How we measure 'reads'.

Convex Optimization — Boyd & Vandenberghe Unconstrained minimization • terminology and assumptions • applies to special class of convex functions (‘self-concordant’ functions) • developed to analyze polynomial-time interior-point methods for convex optimizationFile Size: KB. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): In this paper, we introduce the notion of a self-concordant convex-concave function, establish basic properties of these functions and develop a path-following interior point method for approximating saddle points of “good enough ” convex-concave functions – those which admit natural self-concordant convex.

In this paper we propose a long-step logarithmic barrier function method for convex quadratic programming with linear equality constraints. After a reduction of the barrier parameter, a series of long steps along projected Newton directions are taken until the iterate is in the vicinity of the center associated with the current value of the barrier by: The book concludes with a discussion of the computational tractability of convex programs, and of using interior point methods to solve them.

The prerequisites for reading this book include a class in linear/mathematical programming, although an enthusiast could get through it with only a linear algebra and analysis background. Nesterov, A. Nemirovski, as summarized in their book Interior-Point Polynomial Algorithms in Convex Programming, SIAM Studies in Applied Mathematics, Here are more recent () lecture notes for a course given by Arkadi Nemirovski, entitled "Interior Point Polynomial Time Methods in Convex Programming": PDF link.

Actually, this was a major challenge. At the time only the theory of interior-point methods for linear optimization was polished enough to be explained to students.

The general theory of self-concordant functions had appeared in print only once in the form of research monograph [12]. Actually, this was a major challenge. At the time only the theory of interior-point methods for linear optimization was polished enough to be explained to students.

The general theory of self-concordant functions had appeared in print only once in the form of research monograph [12]. The book contains new and important results in the general theory of convex programming, e.g., their "conic" problem formulation in which duality theory is completely symmetric.

For each algorithm described, the authors carefully derive precise bounds on the computational effort required to solve a given family of problems to a given by: Here is a book devoted to well-structured and thus efficiently solvable convex optimization problems, with emphasis on conic quadratic and semidefinite programming.

The authors present the basic theory underlying these problems as well as their numerous applications in engineering, including synthesis of filters, Lyapunov stability analysis, and structural design.

The results on self-concordant functions and self-concordant barriers allow us to develop the rst poly-nomial interior point scheme - the path-following one; on the qualitative level, the scheme was presented in Lecture I.

Situation Let GˆR nbe a closed and bounded convex domain, and let c2R, c6= 0. In what follows we deal.A new method is proposed for the linesearch procedure in logarithmic barrier function and other interior point methods for convex quadratically constrained quadratic programming problems, which includes linear and quadratic programming as special by: 1.EFFICIENT INTERIOR POINT METHODS 8 R.

C. Monteiro and I. Adler, An Extension of Karmarkar Type Algorithm to a Class of Convex Separable Programming Problems with Global Linear Rate of Convergence, Math. Oper. Res. (). 9 Ju. E. Nesterov and A.

S. Nemirovsky, Self-Concordant Functions and Polynomial-Time Methods in Convex Cited by: