A new line-search step based on the Weierstrass -function for minimizing a class of logarithmic barrier functions

This article is concerned with line-search procedures for a class of problems with certain nonlinear constraints. The class includes as special cases linear and convex quadratic programming problems, entropy programming problems and minimization problems over the cone of positive semidefinite matrices, [1, 2, 18, 7]. For solving a constrained optimization problem of the form minff 0 (x) j f i (x) 0 for 1 i mg (1.1) with four times continuously differentiable functions f i , we consider logarithmic barrier functions of the for