In this paper, we first prove that the expansion and contraction steps of the Nelder-Mead simplex algorithm possess a descent property when the objective function is uniformly convex. This property provides some new insights on why the standard Nelder-Mead algorithm becomes inefficient in high dimensions. We then propose an implementation of the Nelder-Mead method in which the expansion, contra...

The Nelder–Mead simplex algorithm, first published in 1965, is an enormously popular direct search method for multidimensional unconstrained minimization. Despite its widespread use, essentially no theoretical results have been proved explicitly for the Nelder–Mead algorithm. This paper presents convergence properties of the Nelder–Mead algorithm applied to strictly convex functions in dimensio...

Electricity demand forecasting model based on single algorithm at least have two problems related to local optima and computational cost. We consider to utilised the hybrid real value genetic algorithm and extended Nelder-Mead to solved local optima and reduced the number of iteration. The model is known as the hybrid Real-Value GA and Extended Nelder-Mead (RVGA-ENM). The GA has been enhanced t...

In this paper, we discuss the training of a tetris playing AI using a combination of Nelder-Mead optimization and genetic algorithms. The core AI consisted of a variable depth look-ahead player optimizing a set of 16 features, built on the core Java code provided by the TA. A set of random scores were optimized using MATLAB’s implementation of Nelder-Mead, fed through a genetic algorithm, then ...

The popular Nelder and Mead algorithm (NM) has four parameters associated to the operations known as reflection, expansion, contraction and shrinkage. The authors set their values to 1, 2, 0.5 and 0.5, respectively, which have been universally used. Here we propose to use NM to calibrate itself. A computational experiment is carried out and results show that the parameter values originally prop...

Combining meta-heuristics with local search methods is one approach that recently has drawn much attention to design more efficient methods for solving continuous global optimization problems. In this paper, a new algorithm called Simplex Coding Genetic Algorithm (SCGA) is proposed by hybridizing genetic algorithm and simplexbased local search method called Nelder-Mead method. In the SCGA, each...

This chapter presents the Nelder–Mead simplex method and the Broyden– Fletcher–Goldfarb–Shanno (BFGS) method for finite-element-model updating. The methods presented have been tested on a simple beam and an unsymmetrical H-shaped structure. It was noted that, on average, the Nelder–Mead simplex method gives more accurate results than did the BFGS method. This is mainly because the BFGS method r...