Consider the constrained problem:

minimizexeln f(x) (3) subject to XES Let {cx} denote a sequence of positive real numbers satisfying (i) Ck+1 > c. for all k, and (ii) C +0. Let P(x) be a penalty function satisfying (i) P(x) = 0 if x S, and (ii) P(x) > 0 if x # S. In addition, let qc,x):= f(x) + cP(x). Let e be a positive real number, and let {xx} be a sequence such that each xk satisfies qck,xk) c. for all k, and (ii) C +0. Let P(x) be a penalty function satisfying (i) P(x) = 0 if x S, and (ii) P(x) > 0 if x # S. In addition, let qc,x):= f(x) + cP(x). Let e be a positive real number, and let {xx} be a sequence such that each xk satisfies qck,xk)