The problem of minimizing the number of misclassiied points by a plane, attempting to separate two point sets with intersecting convex hulls in n-dimensional real space, is formulated as a linear program with equilibrium constraints (LPEC). This general LPEC can be converted to an exact penalty problem with a quadratic objective and linear constraints. A Frank-Wolfe-type algorithm is proposed f...

In this paper, a novel fuzzy penalty function approach is proposed for solving the constrained optimization problems using evolutionary algorithms. The fuzzy penalty is constructed according to the information contained in individuals so that it can be tuned to reflect the appropriate penalty need for better search. Simulations on ten case studies indicate that the proposed method is very effec...

Online gradient algorithm has been widely used as a learning algorithm for feedforward neural networks training. Penalty is a common and popular method for improving the generalization performance of networks. In this paper, a convergence theorem is proved for the online gradient learning algorithm with penalty, a term proportional to the magnitude of the weights. The monotonicity of the error ...

Numerical solutions obtained by the Meshless Local Petrov-Galerkin (MLPG) method are presented for two dimensional steady-state heat conduction problems. The MLPG method is a truly meshless approach, and neither the nodal connectivity nor the background mesh is required for solving the initial-boundary-value problem. The penalty method is adopted to efficiently enforce the essential boundary co...

Optimum design of structures is achieved while the design variables are continuous and discrete. To reduce the computational work involved in the optimization process, all the functions that are expensive to evaluate, are approximated. To approximate these functions, a semi quadratic function is employed. Only the diagonal terms of the Hessian matrix are used and these elements are estimated fr...

We propose a simple estimation procedure of the number of components of the fundamental frequency model when all the adjacent harmonics are present. The proposed method is based on the penalty function approach like other Information Theoretic Criteria. The new method is shown to be consistent. We compute the probability of wrong estimates of a particular penalty function and propose a resampli...

We propose a Gauss-Newton-type method for nonlinear constrained optimization using the exact penalty introduced recently by André and Silva for variational inequalities. We extend their penalty function to both equality and inequality constraints using a weak regularity assumption, and as a result, we obtain a continuously differentiable exact penalty function and a new reformulation of the KKT...

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...

Many image denoising methods can be characterized as minimizing “loss + penalty,” where the “loss” measures the fidelity of the denoised image to the data, and the “penalty” measures the smoothness of the denoising function. In this paper, we propose two models that use the L1-norm of the pixel updates as the penalty. The L1-norm penalty has the advantage of changing only the noisy pixels, whil...

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 find a feasible solution. The ideas...