Abstract:

For a general nonlinear optimization problem with both inequality and equality constraints, a corollary on the optimization problem with a lp penalty function is studied and proved based on the sequential quadratic programming approach. In particular, the corollary defines the inequality condition for the search direction of the optimization problem. Moreover, it proves that the derived search direction is a descent direction of the penalty function in the original problem by determining the range of penalty parameter.

Key words: nonlinearly constrained optimization; sequential quadratic programming; penalty function; directional derivative