The Nelder-Mead simplex method is an optimization routine that works well with irregular objective functions. For a function of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$n$$</EquationSource> </InlineEquation> parameters, it compares the objective function at the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$n+1$$</EquationSource> </InlineEquation> vertices of a simplex and updates the worst vertex through simplex search steps. However, a...</equationsource></inlineequation></equationsource></inlineequation>

Invasive Weed Optimization (IWO) algorithm is a simple but powerful algorithm which is capable of solving general multi-dimensional, linear and nonlinear optimization problems with appreciable efficiency. Recently IWO algorithm is being used in several engineering design owing to its superior...

The optimal dispatching of cascade Hydro Power Plants is known as a complex optimization problem. In order to solve this problem the authors have applied an adapted differential evolution algorithm by using a fixed and dynamic population size. According to the dynamic population size, the...

In solving certain optimization problems, the corresponding Lagrangian dual problem is often solved simply because in these problems the dual problem is easier to solve than the original primal problem. Another reason for their solution is the implication of the weak duality theorem which...

In recent years, numerical and experimental investigations on the draft tube performance have confirmed the importance of the inlet swirling flow created by the runner vanes. The results indicate that it is still a challenge to get the optimal flow distribution at the draft tube inlet which...

Order-value optimization (OVO) is a generalization of the minimax problem motivated by decision-making problems under uncertainty and by robust estimation. New optimality conditions for this nonsmooth optimization problem are derived. An equivalent mathematical programming problem with...