Approximation methods for complex polynomial optimization

نویسندگان

  • Bo Jiang
  • Zhening Li
  • Shuzhong Zhang
چکیده

Complex polynomial optimization problems arise from real-life applications including radar code design, MIMO beamforming, and quantum mechanics. In this paper, we study complex polynomial optimization models whereby the objective function takes one of the following three forms: (1) multilinear; (2) homogeneous polynomial; (3) a conjugate symmetric form. On the constraint side, the decision variables belong to one of the following three sets: (1) the m-th roots of complex unity; (2) the complex unity; (3) the Euclidean sphere. We first discuss the multilinear objective function. Polynomial-time approximation algorithms are proposed for such problems with assured worst-case performance ratios, which depend only on the dimensions of the model. Then we introduce complex homogenous polynomial functions and establish key linkages between complex multilinear form and the complex polynomial functions. Approximation algorithms for the above-mentioned complex polynomial optimization models with worst-case performance ratios are presented.

برای دانلود رایگان 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

A method to obtain the best uniform polynomial approximation for the family of rational function

In this article, by using Chebyshev’s polynomials and Chebyshev’s expansion, we obtain the best uniform polynomial approximation out of P2n to a class of rational functions of the form (ax2+c)-1 on any non symmetric interval [d,e]. Using the obtained approximation, we provide the best uniform polynomial approximation to a class of rational functions of the form (ax2+bx+c)-1 for both cases b2-4a...

متن کامل

Comparative Analysis of Approximation Methods in Electromagnetic Design

Design optimization of complex electromagnetic devices such as antennas with volumetric material and conductor variations require high computational resources. This burden can be reduced by introducing cost-effective surrogate models into the design optimization framework. Here we present a comparative analysis of various surrogate modeling techniques for material design studies of electromagne...

متن کامل

A novel technique for a class of singular boundary value problems

In this paper, Lagrange interpolation in Chebyshev-Gauss-Lobatto nodes is used to develop a procedure for finding discrete and continuous approximate solutions of a singular boundary value problem. At first, a continuous time optimization problem related to the original singular boundary value problem is proposed. Then, using the Chebyshev- Gauss-Lobatto nodes, we convert the continuous time op...

متن کامل

Accurate And Efficient Global Approximation using Adaptive Polynomial RSM for Complex Mechanical and Vehicular Performance Models

Global approximation using metamodel for complex mathematical function or computer model over a large variable domain is often needed in sensibility analysis, computer simulation, optimal control, and global design optimization of complex, multiphysics systems. To overcome the limitations of the existing response surface (RS), surrogate or metamodel modeling methods for complex models over larg...

متن کامل

Continuous Discrete Variable Optimization of Structures Using Approximation Methods

Optimum design of structures is achieved while the design variables are continuous and discrete. To reduce the computational work involved in the optimization process, all the functions that are expensive to evaluate, are approximated. To approximate these functions, a semi quadratic function is employed. Only the diagonal terms of the Hessian matrix are used and these elements are estimated fr...

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

عنوان ژورنال:
  • Comp. Opt. and Appl.

دوره 59  شماره 

صفحات  -

تاریخ انتشار 2014