this paper introduces a technique for controlling a class of uncertain chaotic systems using an adaptive fuzzy proportional-integrator-derivative (pid) controller with h∞ tracking performance. the purpose of this work is to achieve optimal tracking performance of the controller using backtracking search algorithm (bsa). bsa, which is a novel heuristic algorithm, has an easy structure with singl...

We propose an algorithm for nonlinear optimization that employs both trust region techniques and line searches Unlike traditional trust region methods our algorithm does not resolve the subproblem if the trial step results in an increase in the objective function but instead performs a backtracking line search from the failed point Backtracking can be done along a straight line or along a curve...

where | · | denotes the `1 norm, ‖·‖ denotes the `2 norm, A is a matrix, b is a vector, and μ is a scalar parameter. This problem is of the form (1) with g(z) = μ|z|, and f(z) = 12‖z− b‖ . More generally, any problem of the form (1) can be solved by FASTA, provided the user can provide function handles to f, g, A and A . The solver FASTA contains numerous enhancements of FBS to improve converge...

Newton’s algorithm and some of its variations are often used to find global minima of real valued functions. We propose another such variation and prove its local quadratic convergence. We combine this with Armijo type line search method to produce global convergence, which is eventually quadratic, for the important class of strictly convex functions. Computational performance on some standard ...

Recently, Fan [4, Math. Comput., 81 (2012), pp. 447-466] proposed a modified Levenberg-Marquardt (MLM) method for nonlinear equations. Using a trust region technique, global and cubic convergence of the MLM method is proved [4] under the local error bound condition, which is weaker than nonsingularity. The purpose of the paper is to investigate the convergence properties of the MLM method with ...

This paper proposes a predictor-corrector primal-dual interior point method which introduces line search procedures IPLS in both the predictor and corrector steps. The Fibonacci search technique is used in the predictor step, while an Armijo line search is used in the corrector step. The method is developed for application to the economic dispatch ED problem studied in the field of power system...

In this paper, we consider the method for solving finite minimax problems. By using exponential penalty function to smooth problems, a new three-term nonlinear conjugate gradient is proposed which generates sufficient descent direction at each iteration. Under standard assumptions, global convergence of with Armijo-type line search established. Numerical results are given illustrate that can ef...

Recently, Zhang 2006 proposed a three-term modified HS TTHS method for unconstrained optimization problems. An attractive property of the TTHS method is that the direction generated by the method is always descent. This property is independent of the line search used. In order to obtain the global convergence of the TTHS method, Zhang proposed a truncated TTHS method. A drawback is that the num...

In this paper, we aim to solve an inverse robust optimization problem, in which the parameters in both the objective function and the robust constraint set need to be adjusted as little as possible so that a known feasible solution becomes the optimal one. We formulate this inverse problem as a minimization problem with a linear equality constraint, a second-order cone complementarity constrain...