An affine scaling reduced preconditional conjugate gradient path method for linear constrained optimization (Q879466)

The author presents an affine scaling reduced preconditional conjugate gradient path approach in association with a nonmonotonic interior backtracking line search technique for solving a nonlinear optimization problem subject to both linear equality and linear inequality constraints. Namely, in order to avoid the difficulties of the strictly feasible constraints, the author introduces the affine scaling matrix and reduced Hessian to generate an affine scaling preconditional conjugate gradient path in which the curvilinear path search is used instead of the trust region strategy. Employing the affine scaling preconditional conjugate gradient to form the curvilinear path and using the interior backtracking line search technique, each iterate switches to a trial step for strict interior feasibility. The nonmonotone criterion is used to speed up the convergence progress in the contours of an objective function with large curvature. It is proved that the proposed algorithm is globally convergent and has a local superlinear convergence rate under some reasonable smooth conditions.