On Polyhedral Approximations of the Second-Order Cone
نویسندگان
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 ∑
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 کاملOn 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 کاملApproximate 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 کاملOn 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 کاملMixed 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 کاملذخیره 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 ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Math. Oper. Res.
دوره 26 شماره
صفحات -
تاریخ انتشار 2001