The following information was submitted:
Transactions: WSEAS TRANSACTIONS ON MATHEMATICS
Transactions ID Number: 29-288
Full Name: Iurie Caraus
Position: Associate Professor
Age: ON
Sex: Male
Address: Mateevici 60 str.,
Country: MOLDOVA
Tel:
Tel prefix:
Fax:
E-mail address: caraush@usm.md
Other E-mails:
Title of the Paper: A CUTTING PLANE METHOD FOR SOLVING CONVEX OPTIMIZATION PROBLEMS OVER THE CONE OF NONNEGATIVE POLYNOMIALS
Authors as they appear in the Paper: Ion NECOARA
Email addresses of all the authors: i.necoara@yahoo.com
Number of paper pages: 10
Abstract: Many practical problems can be formulated as convex optimization problems over the cone of nonnegative univariate polynomials. We use a cutting plane method for solving this type of optimization problems in primal form. Therefore, we must be able to verify whether a polynomial is nonnegative, i.e. if it does not have real roots or all real roots are multiple of even order. In this paper an efficient method is derived to determine a scalar value for which the polynomial is negative and in the case that such a value exists a feasible cut is constructed. Our method is based on Sturm theorem, which allows to determine the number of distinct roots of a polynomial on a given interval, in combination with the bisection method. For numerical stability we construct the associated Sturm sequence using Chebyshev polynomials, and thus we can work with high degree polynomials, up to hundreds. Numerical results show the efficiency of our new approach.
Keywords: convex optimization problems over the cone of nonnegative polynomials, cutting plane method, Chebyshev polynomials, Sturm sequence, feasible cut
EXTENSION of the file: .pdf
Special (Invited) Session: Reduction Methods for Approximate Solution of Singular Integro-Differential Equations in Lebesgue spaces
Organizer of the Session: 612-231
How Did you learn about congress:
IP ADDRESS: 87.255.70.165
