Survey of penalty, exact-penalty and multiplier methods from 1968 to 1993

Existence and stability of exact penalty for optimization problems with mixed constraints

“…See, for example, [1][2][3][4][5][6] and the references mentioned there. A penalty function is said to have the exact penalty property if there is a a constant Λ > 0 such that for any penalty coefficient larger than Λ, solutions of the unconstrained penalized problem are solutions of the corresponding constrained problem.…”

Existence of Exact Penalty and Its Stability for Nonconvex Constrained Optimization Problems in Banach Spaces

“…A penalty function is said to have the exact penalty property [1,3,5,9] if there is a penalty coefficient for which a solution of an unconstrained penalized problem is a solution of the corresponding constrained problem. We study two constrained nonconvex minimization problems with Lipschitzian (on bounded sets) cost functions.…”

“…For more discussions and various applications of exact penalization to various constrained optimization problems see [1,3,5,9,14].…”

Existence of Exact Penalty for Constrained Optimization Problems in Metric Spaces

“…A penalty function is said to have the exact penalty property [1,3,5,9] if there is a penalty coefficient for which a solution of an unconstrained penalized problem is a solution of the corresponding constrained problem. In this paper we establish sufficient conditions for the exact penalty property.…”