loading page

Fractional order log barrier interior point method in ℓp− norm minimization problems
  • Eliana Contharteze Grigoletto
Eliana Contharteze Grigoletto
Universidade Estadual Paulista Julio de Mesquita Filho - Campus de Botucatu

Corresponding Author:[email protected]

Author Profile

Abstract

In this work we include the Caputo fractional derivatives in the first order optimality conditions of Karush-Kuhn-Tucker for the barrier optimization problem to minimize ℓ p − norms for both super-Gaussian ( 1 < p < 2 ) and sub-Gaussian ( 2 < p < ∞ ) cases. The optimality conditions associated with the Newton method provides search directions to the so-called fractional order log barrier interior point method. As a result of this methodology, we apply the fractional order log barrier interior point method to curve fitting data on the mechanical properties of polypropylene composites, and compare it with the standard log barrier interior point method. Numerical experiments show that the fractional order log barrier interior point method can be used without impeding the convergence of the method and, in some cases, presents less residual norm and number of iterations.