In this study a modified entropy-based measure is presented for evaluating the serviceability level of water distribution networks in which the hydraulic uncertainties (flow rates in pipes) as well as the uncertainties due to mechanical parameters (failure probabilities of links) are considered simultaneously. In the proposed entropy calculation method, the connectivity order of the network dem...

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...

We shall assume that each problem function has sufficiently many continuous derivatives for any implicit assumptions that we make to hold. One of the most successful tools for solving problems of the form NLP and SIP is the penalty function. A penalty-function approach replaces the relevant problem by a suitably weighted combination of the objective function f(x) and functions representing viol...

We present a stochastic approximation algorithm based on penalty function method and a simultaneous perturbation gradient estimate for solving stochastic optimisation problems with general inequality constraints. We present a general convergence result that applies to a class of penalty functions including the quadratic penalty function, the augmented Lagrangian, and the absolute penalty functi...

We present a stochastic approximation algorithm based on penalty function method and a simultaneous perturbation gradient estimate for solving stochastic optimization problems with general inequality constraints. We present a general convergence result that applies to a class of penalty functions including the quadratic penalty function, the augmented Lagrangian, and the absolute penalty functi...