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 ...

A penalty framework for globally solving mixed-integer nonlinear programming problems is presented. Both integrality constraints and nonlinear constraints are handled separately by hyperbolic tangent penalty functions. The preliminary numerical experiments show that the proposed penalty approach is effective and the hyperbolic tangent penalties compete with other popular penalties.

The theory of increasing positively homogeneous functions deened on the positive orthant is applied to the class of decreasing functions. A multiplicative version of the inf-convolution operation is studied for decreasing functions. Modiied penalty functions for some constrained optimization problems are introduced which are in general nonlinear with respect to the objective function of the ori...

A novel approach to fuzzy clustering for image segmentation is described. The fuzzy C-means objective function is generalized to include a spatial penalty on the membership functions. The penalty term leads to an iterative algorithm that is only slightly different from the original fuzzy C-means algorithm and allows the estimation of spatially smooth membership functions. To determine the stren...

In this note we derive a geometric formulation for equality constrained problems of an ideal penalty function This di erentiable penalty function requires no parameter esti mation or adjustment has numerical conditioning similar to that of the target function from which it is constructed and also has the desirable property that the strict second order constrained minima of the target function a...

In this paper we discuss the use of non-stationary penalty functions to solve general nonlinear programming problems (NP) using real-valued GAs. The non-stationary penalty is a function of the generation number; as the number of generations increases so does the penalty. Therefore, as the penalty increases it puts more and more selective pressure on the GA to nd a feasible solution. The ideas p...

In this paper, we considered the role of penalty when the higher-order conjugate gradient method (HCGM) was used as a computational scheme for the minimization of penalised cost functions for optimal control problems described by linear systems and integral quadratic costs. For this family of commonly encountered problems, we find out that the conventional penalty methods require very large pen...