On Polyhedral Approximations of the Second-Order Cone

نویسندگان

  • Aharon Ben-Tal
  • Arkadi Nemirovski
چکیده

We demonstrate that a conic quadratic problem min x { ex ∣Ax ≥ b, ‖A`x− b`‖2 ≤ c` x− d`, ` = 1, ...,m } , ‖y‖2 = √ yT y, (CQP) is “polynomially reducible” to Linear Programming. We demonstrate this by constructing, for every ∈ (0, 12 ], an LP program (explicitly given in terms of and the data of (CQP)) min x,u { ex ∣P ( x u ) + p ≥ 0 } (LP) with the following properties: (i) the number dim x+ dim u of variables and the number dim p of constraints in (LP) do not exceed O(1) [ dim x+ dim b+ m ∑

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

Analytic Solution for Hypersonic Flow Past a Slender Elliptic Cone Using Second-Order Perturbation Approximations

An approximate analytical solution is obtained for hypersonic flow past a slender elliptic cone using second-order perturbation techniques in spherical coordinate systems. The analysis is based on perturbations of hypersonic flow past a circular cone aligned with the free stream, the perturbations stemming from the small cross-section eccentricity. By means of hypersonic approximations for the ...

متن کامل

On polyhedral approximations in p-order cone programming

This paper discusses the use of polyhedral approximations in solving of p-order cone programming (pOCP) problems, or linear problems with p-order cone constraints, and their mixed-integer extensions. In particular, it is shown that the cutting-plane technique proposed in Krokhmal and Soberanis (2010) for a special type of polyhedral approximations of pOCP problems, which allows for generation o...

متن کامل

Approximate cone factorizations and lifts of polytopes

In this paper we show how to construct inner and outer convex approximations of a polytope from an approximate cone factorization of its slack matrix. This provides a robust generalization of the famous result of Yannakakis that polyhedral lifts of a polytope are controlled by (exact) nonnegative factorizations of its slack matrix. Our approximations behave well under polarity and have efficien...

متن کامل

On the accuracy of uniform polyhedral approximations of the copositive cone

We consider linear optimization problems over the cone of copositive matrices. Such conic optimization problems, called copositive programs, arise from the reformulation of a wide variety of difficult optimization problems. We propose a hierarchy of increasingly better outer polyhedral approximations to the copositive cone. We establish that the sequence of approximations is exact in the limit....

متن کامل

Mixed integer programming with a class of nonlinear convex constraints

We study solution approaches to a class of mixed-integer nonlinear programming problems that arise from recent developments in risk-averse stochastic optimization and contain second-order and p-order cone programming as special cases. We explore possible applications of some of the solution techniques that have been successfully used in mixed-integer conic programming and show how they can be g...

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:
  • Math. Oper. Res.

دوره 26  شماره 

صفحات  -

تاریخ انتشار 2001