A primal-dual modified log-barrier method for inequality constrained nonlinear optimization

Joshua D. Griffin, Riadh Omheni

Abstract: We present a primal–dual modified log-barrier algorithm to solve inequality constrained nonlinear optimization problems. Basically, the algorithm is a Newton-like method applied to a perturbation of the optimality system that follows from a reformulation of the initial problem by introducing a modified log-barrier function to handle inequality constraints. The algorithm uses an outer/inner iteration scheme and the globalization is performed in the primal–dual space by means of a new primal–dual merit function. The robustness and efficiency of the algorithm is improved using quadratic extrapolation. The numerical performance of the new method is illustrated by comparing it with a primal–dual classical log-barrier method and two well-established interior-point solvers on two sets of problems from COPS and Hock–Schittkowski collections, including a set of problems that exhibits degeneracy.