A new projective exact penalty function method is proposed for the equivalent reduction of constrained optimization problems to nonsmooth unconstrained ones. In the method, the
original objective function is extended to infeasible points by summing its value at the projection of an infeasible point on the feasible set with the distance to the projection. The equivalence means that local and global minimums of the problems coincide. Nonconvex sets with multivalued projections are admitted, and the objective function may be lower semicontinuous. The obtained problem is solved by a branch and bound method combined with local optimization. The particular case of convex problems is included. So the method does not assume the existence of the objective function outside the allowable area and does not require the selection of the penalty coefficient.
Norkin V.I. (2022). The projective exact penalty method for general constrained optimization. Preprint. V.M.Glushkov Institute of Cybernetics, Kyiv, October 05, 2022