For semi-infinite programming (SIP), we consider a class of smoothed penalty functions, which approximate the exact <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$l_\rho (0\rho \le 1)$$</EquationSource> </InlineEquation> penalty functions. On base of the smoothed penalty function, we present a feasible penalty algorithm for solving SIP. Without any boundedness condition...</equationsource></inlineequation>

For inequality constrained optimization problem, we show the existence of local saddle point of generalized augmented Lagrangian under weak second-order sufficient conditions which are weaker than the second-order sufficient conditions in the literature. We further discuss the existence of...