Semidefinite Approximations for Global Unconstrained Polynomial Optimization

نویسندگان
چکیده

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

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Semidefinite Approximations for Global Unconstrained Polynomial Optimization

We consider the problem of minimizing a polynomial function on R, known to be hard even for degree 4 polynomials. Therefore approximation algorithms are of interest. Lasserre [15] and Parrilo [23] have proposed approximating the minimum of the original problem using a hierarchy of lower bounds obtained via semidefinite programming relaxations. We propose here a method for computing tight upper ...

متن کامل

Converging Semidefinite Bounds for Global Unconstrained Polynomial Optimization

We consider here the problem of minimizing a polynomial function on Rn. The problem is known to be hard even for degree 4. Therefore approximation algorithms are of interest. Lasserre [11] and Parrilo [16] have proposed approximating the minimum of the original problem using a hierarchy of lower bounds obtained via semidefinite programming relaxations. We propose here a method for computing a c...

متن کامل

Convergent Semidefinite Programming Relaxations for Global Bilevel Polynomial Optimization Problems

In this paper, we consider a bilevel polynomial optimization problem where the objective and the constraint functions of both the upper and the lower level problems are polynomials. We present methods for finding its global minimizers and global minimum using a sequence of semidefinite programming (SDP) relaxations and provide convergence results for the methods. Our scheme for problems with a ...

متن کامل

Semidefinite Approximations of the Polynomial Abscissa

Given a univariate polynomial, its abscissa is the maximum real part of its roots. The abscissa arises naturally when controlling linear differential equations. As a function of the polynomial coefficients, the abscissa is Hölder continuous, and not locally Lipschitz in general, which is a source of numerical difficulties for designing and optimizing control laws. In this paper we propose simpl...

متن کامل

Global Optimality Principles for Polynomial Optimization Problems over Box or Bivalent Constraints by Separable Polynomial Approximations∗

In this paper we present necessary conditions for global optimality for polynomial problems over box or bivalent constraints using separable polynomial relaxations. We achieve this by completely characterizing global optimality of separable polynomial problems with box as well as bivalent constraints. Then, by employing separable polynomial under-estimators, we establish sufficient conditions f...

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

ژورنال

عنوان ژورنال: SIAM Journal on Optimization

سال: 2005

ISSN: 1052-6234,1095-7189

DOI: 10.1137/04060562x