[PDF] Top 20 New Variants of Newton’s Method for Nonlinear Unconstrained Optimization Problems

... Newton’s method ( ), cen- troidal mean Newton’s method ( ), logarithmic mean Newton’s method (LMNM) respectively to com- pute the extrememum of the function given in Table ... See full document

... scalar nonlinear equations and unconstrained optimization ...Newton’s method which may converge slowly or even ...Newton’s method for the case of nonlinear equations or for the ... See full document

... the new conjugate gradient formula and algorithm method presented, in section 3, we showed the descent condition and the global convergence proof of our new ... See full document

... Jacobian New- ton Iterative Method for solving nonlinear elliptic ...proposed method is demonstrated through numerical ...our method with Newton Iterative Method is also ... See full document

... In this paper, we prove the global convergence of the Perry-Shanno’s memoryless quasi-Newton (PSMQN) method with a new inexact line search when applied to nonconvex unconstrained minimization ... See full document

... multiple root of f (x) = 0. Then the problem of finding a multiple root is reduced to the problem of finding a simple root of the transformed equation µ(x), and thus any iterative method can be used to maintain its ... See full document

... The nonlinear conjugate gradient method is one of the best methods to solve uncon- strained optimization ...of unconstrained optimization al- gorithms which is characterized by low ... See full document

... DFP update is a rank- two update and has become the best known of the Quasi-Newton algorithms. The DFP update formula was originally proposed by Davidon [6] and developed later by Fletcher and Powell [7]. Hence it ... See full document

... the Newton-Raphson and Mean-centre al- gorithms for obtaining the optimum and the exploration of near optimal settings within the optimal ...previous method and then introduces several other steps, thereby ... See full document

... a new conjugate gradient method using an acceleration scheme for solving large-scale unconstrained ...proposed method with a Wolfe line search is ...given method is competitive for ... See full document

... with/without nonlinear mapping gives similar ...no nonlinear mapping, we have the possibility of directly solving bigger optimization ...our method cannot be ...region method for ... See full document

... a new algorithmic approach for the optimal realization of FWL PID controller ...the optimization can be decoupled into two unconstrained problems with a maximum of four independent ...An ... See full document

... region methods; see, e.g., [9,17,18]. Line search methods refer to a procedure in which one moves along a (descent) direction as long as a sufficient reduc- tion in the objective is achieved. On the other hand, in the ... See full document

... BFGS method is the most successful one among all the quasi-Newton ...any new quasi-Newton method that not only possess global convergence but also superior than the BFGS method ... See full document

... introduced Newton iteration as a genetic operators of the algorithm and iteratived the progeny individuals with the probability P, the new iteration value instead of the parent to join their ...compatible ... See full document

... nonsmoothing Newton method is one of the important methods for solving ...semi-smoothing Newton method and feasible methods ...asymptotically Newton method for mixed complemen- ... See full document

... each method, we plot the fraction P of problems for which the method is within a factor τ of the best ...test problems for which a method is fastest; the right side gives the percentage ... See full document

... a new meta-heuristic method is proposed by combining particle swarm optimization (PSO) and gravitational search in a coherent ...meta-heuristic method for constrained optimization ... See full document

... a new modified regularized Newton algorithm by using trust region ([14], [21], [22], [24]) technique, and prove the global convergence of the new algorithm under some suitable ... See full document

... [1] M. Al-Baali, “Descent Property and Global Convergence of the Fletcher-Reeves Method with Inexact Line Search,” IMA Journal of Numerical Analysis, Vol. 5, No. 1, 1985, pp. 121-124. doi:10.1093/imanum/5.1.121 ... See full document