Abstract Step sizes is very important for a global convergence gradient method solving the problems of unconstrained optimization. The new step formulas techniques proposed, key idea used in construction algorithm to approximate Hessian by suitable diagonal matrix, which has been found be most efficient this paper. Under weaker conditions, we define convergences proposed methods. In addition, w...

The tuned liquid column damper (TLCD) having a uniform cross-sectional tube of U-shaped, occupied with liquid is used as a vibrational response mitigation device. The tuned liquid column ball damper (TLCBD) is a modified TLCD, where, an immovable orifice, positioned at the middle part of the horizontal portion, is replaced by a metal ball. Different studies on the unconstrained optimization per...

In this paper, we review the trust region algorithms for nonlinear optimization. The philosophy and the fundamental ideas of trust region algorithms are discussed. Model algorithms for unconstrained optimization, constrained optimization, and nonsmooth optimization are given. Main techniques for global convergence and local superlinear convergence are analyzed.

This paper presents a numerical solution of a class of fractional optimal control problems (FOCPs) in a bounded domain having a noise function by the spectral Ritz method‎. ‎The Bernstein polynomials with the fractional operational matrix are applied to approximate the unknown functions‎. ‎By substituting these estimated functions into the cost functional‎, ‎an unconstrained nonlinear optimizat...