A line search penalty-free SQP method for equality-constrained optimization without Maratos effect

A line search penalty-free sequential quadratic programming method is proposed for nonlinear equality-constrained optimization. Generally, feasible directions are used to minimize the measurement of the constraint violation in order to deal with the inconsistency in the linearized constraints while optimal directions aim to improve the measure of optimality. A basic feature of the proposed method is that a line search direction that is some convex combination of a feasible direction and an optimal direction is utilized at each iteration, making either the value of the Lagrangian function or the measure of constraint violation sufficiently reduced. Global convergence of the method is analyzed without the feasibility restoration phase. Under the usual assumptions the method is shown to be superlinearly convergent locally without the second-order correction and hence the Maratos effect can be avoided. Numerical experiments on several examples illustrate the local behavior of the method.