Particle swarm optimization (PSO), genetic algorithm (GA), and nonlinear simplex method (SOM) are some of the most prominent gradient-free algorithms in engineering. When it comes to a common group electromagnetic problems wherein less than 10 parameters present problem domain, SOM features faster convergence rate vs PSO GA. Nevertheless, GA still outperform by having more accuracy finding glob...

We prove that the Nelder–Mead simplex method converges in sense vertices converge to a common limit point with probability of one. The result may explain practical usefulness method.

The purpose of this paper is to present a new approach for solving linear programming, which has some interesting theoretical properties. In each step of the iteration, we trace a direction completely different from primal simplex method, dual simplex method, primal-dual method and interior point method. The new method is impervious to primal degeneracy and can reach a pair of exact primal and ...

In real optimization problems, usually the analytical expression of the objective function is not known, nor its derivatives, or they are complex. In these cases it becomes essential to use optimization methods where the calculation of the derivatives, or the verification of their existence, is not necessary: the Direct Search Methods or Derivative-free Methods are one solution. When the proble...

‎This paper describes a new optimization method for solving continuous semi-infinite linear problems‎. ‎With regard to the dual properties‎, ‎the problem is presented as a measure theoretical optimization problem‎, ‎in which the existence of the solution is guaranteed‎. ‎Then‎, ‎on the basis of the atomic measure properties‎, ‎a computation method was presented for obtaining the near optimal so...