In this paper, we give a smoothing approximation to the lower order exact penalty functions for inequality-constrained optimization problems. Error estimations are obtained among the optimal objective function values of the smoothed penalty problem, of the nonsmooth penalty problem and of the original optimization problem. An algorithm based on the smoothed penalty function is presented, which ...

In this paper, an optimal PID tuning method is proposed for a class of two-link manipulators. particular, the control specifications manipulators are considered. By modeling into state constraints, problem converted to parameters selection with constraints. An exact penalty function based then utilized handle The superior over existing verified by carrying out numerical example.

The exactness of the penalization for the exact l1 penalty function method used for solving nonsmooth constrained optimization problems with both inequality and equality constraints are presented. Thus, the equivalence between the sets of optimal solutions in the nonsmooth constrained optimization problem and its associated penalized optimization problem with the exact l1 penalty function is es...

We reformulate the zero-norm minimization problem as an equivalent mathematical program with equilibrium constraints and establish that its penalty problem, induced by adding the complementarity constraint to the objective, is exact. Then, by the special structure of the exact penalty problem, we propose a decomposition method that can seek a global optimal solution of the zero-norm minimizatio...

A new global optimization method combining genetic algorithm and Hooke-Jeeves method to solve a class of constrained optimization problems is studied in this paper. We first introduce the quadratic penalty function method and the exact penalty function method to transform the original constrained optimization problem with general equality and inequality constraints into a sequence of optimizati...

We consider a class of constrained optimization problems with a possibly nonconvex non-Lipschitz objective and a convex feasible set being the intersection of a polyhedron and a possibly degenerate ellipsoid. Such problems have a wide range of applications in data science, where the objective is used for inducing sparsity in the solutions while the constraint set models the noise tolerance and ...

We propose a method for solving nonlinear second-order cone programs (SOCPs), based on a continuously differentiable exact penalty function. The construction of the penalty function is given by incorporating a multipliers estimate in the augmented Lagrangian for SOCPs. Under the nondegeneracy assumption and the strong second-order sufficient condition, we show that a generalized Newton method h...