Advances in convex optimization: conic programming

نویسنده

  • Arkadi Nemirovski
چکیده

During the last two decades, major developments in convex optimization were focusing on conic programming, primarily, on linear, conic quadratic and semidefinite optimization. Conic programming allows to reveal rich structure which usually is possessed by a convex program and to exploit this structure in order to process the program efficiently. In the paper, we overview the major components of the resulting theory (conic duality and primal-dual interior point polynomial time algorithms), outline the extremely rich “expressive abilities” of conic quadratic and semidefinite programming and discuss a number of instructive applications. Mathematics Subject Classification (2000). Primary 90C22,90C25,90C51,90C90; Secondary

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Exact Conic Programming Relaxations for a Class of Convex Polynomial Cone Programs

In this paper, under a suitable regularity condition, we establish that a broad class of conic convex polynomial optimization problems, called conic sum-of-squares convex polynomial programs, exhibits exact conic programming relaxation, which can be solved by various numerical methods such as interior point methods. By considering a general convex cone-program, we give unified results that appl...

متن کامل

On Verified Numerical Computations in Convex Programming

This survey contains recent developments for computing verified results of convex constrained optimization problems, with emphasis on applications. Especially, we consider the computation of verified error bounds for non-smooth convex conic optimization in the framework of functional analysis, for linear programming, and for semidefinite programming. A discussion of important problem transforma...

متن کامل

Convex Optimization Models: An Overview

1.1. Lagrange Duality . . . . . . . . . . . . . . . . . . p. 2 1.1.1. Separable Problems – Decomposition . . . . . . . p. 7 1.1.2. Partitioning . . . . . . . . . . . . . . . . . . p. 9 1.2. Fenchel Duality and Conic Programming . . . . . . . . p. 10 1.2.1. Linear Conic Problems . . . . . . . . . . . . . p. 15 1.2.2. Second Order Cone Programming . . . . . . . . . p. 17 1.2.3. Semidefinite Progr...

متن کامل

A Short Proof of Strassen’s Theorem Using Convex Analysis

We give a simple proof of Strassen’s theorem on stochastic dominance using linear programming duality, without requiring measure-theoretic arguments. The result extends to generalized inequalities using conic optimization duality and provides an additional, intuitive optimization formulation for stochastic dominance.

متن کامل

Space tensor conic programming

Space tensors appear in physics and mechanics, and they are real physical entities. Mathematically, they are tensors in the three-dimensional Euclidean space. In the research of diffusion magnetic resonance imaging, convex optimization problems are formed where higher order positive semi-definite space tensors are involved. In this short paper, we investigate these problems from the viewpoint o...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2002