A derivative-free algorithm for non-linear optimization with linear equality constraints

Abstract

ABSTRACTWe propose a derivative-free algorithm for solving linear equality constrained non-linear optimization problems, named LECOA. In each iteration of the algorithm, the objective function is approximated by a quadratic model constructed from interpolation points. The choice of the points leaves some degree of freedom in the model taken up by minimizing the Frobenius norm of the change to the Hessian matrix of the model. The new iterate is generally generated by minimizing the model in a trust-region using a null space truncated conjugate gradient method. Numerical results are presented which show that the proposed algorithm competes against some algorithms in the literature. Experiments show that starting with the point that minimizes the infinity norm subject to the linear equality constraints gives excellent results. A limit-type global convergence of the proposed algorithm is proved under some reasonable assumptions.