A norm-relaxed SQP method of strongly sub-feasible direction for finely discretized problems from semi-infinite programming

In this paper, we discuss a kind of finely discretized problem from semi-infinite programming. Combining the idea of the norm-relaxed SQP method of strongly sub-feasible direction method with the technique of updating discretization index set, we present a new algorithm with arbitrary initial point for the discussed problem. At each iteration, an improved direction is obtained by solving only one direction finding subproblem, and some appropriate constraints are chosen to reduce the computational cost. Under mild assumptions such as Mangasarian-Fromovitz Constraint Qualification (MFCQ), the proposed algorithm possesses weak global convergence. Finally, some primary numerical experiments are reported.