A Class of Parameter Estimation Methods for Nonlinear Muskingum Model Using Hybrid Invasive Weed Optimization Algorithm

et al. 2020

Conjugate gradient methods are well-known methods which are widely applied in many practical fields. CD conjugate gradient method is one of the classical types. In this paper, a modified three-term type CD conjugate gradient algorithm is proposed. Some good features are presented as follows: (i) A modified three-term type CD conjugate gradient formula is presented. (ii) The given algorithm possesses sufficient descent property and trust region property. (iii) The algorithm has global convergence with the modified weak Wolfe–Powell (MWWP) line search technique and projection technique for general function. The new algorithm has made great progress in numerical experiments. It shows that the modified three-term type CD conjugate gradient method is more competitive than the classical CD conjugate gradient method.

Section: E Muskingum Modelmentioning

confidence: 99%

A Modified Three-Term Type CD Conjugate Gradient Algorithm for Unconstrained Optimization Problems

et al. 2020

“…In this section, the main work is to use Algorithm 1 to numerically estimate the Muskingum model [20], whose definition is as follows:…”

Section: Muskingum Modelmentioning

confidence: 99%

Convergence Analysis of an Improved BFGS Method and Its Application in the Muskingum Model

Yang

2020

The BFGS method is one of the most effective quasi-Newton algorithms for minimization-optimization problems. In this paper, an improved BFGS method with a modified weak Wolfe–Powell line search technique is used to solve convex minimization problems and its convergence analysis is established. Seventy-four academic test problems and the Muskingum model are implemented in the numerical experiment. The numerical results show that our algorithm is comparable to the usual BFGS algorithm in terms of the number of iterations and the time consumed, which indicates our algorithm is effective and reliable.

“…e specific reasons for good performance are stated as follows. e parameter scaling the first two terms of the standard BFGS update is determined to cluster the eigenvalues of Muskingum model [50]: whose symbolic representation is as follows: x 1 is the storage time constant, x 2 is the weight coefficient, x 3 is an extra parameter, I i is the observed inflow discharge, Q i is the observed outflow discharge, n is the total time, and Δt is the time step at time t i (i � 1, 2, . .…”

Section: General Unconstrained Optimisation Problemsmentioning

confidence: 99%

Global Convergence of a Modified Two-Parameter Scaled BFGS Method with Yuan-Wei-Lu Line Search for Unconstrained Optimization

Luo

et al. 2020

The BFGS method is one of the most efficient quasi-Newton methods for solving small- and medium-size unconstrained optimization problems. For the sake of exploring its more interesting properties, a modified two-parameter scaled BFGS method is stated in this paper. The intention of the modified scaled BFGS method is to improve the eigenvalues structure of the BFGS update. In this method, the first two terms and the last term of the standard BFGS update formula are scaled with two different positive parameters, and the new value of yk is given. Meanwhile, Yuan-Wei-Lu line search is also proposed. Under the mentioned line search, the modified two-parameter scaled BFGS method is globally convergent for nonconvex functions. The extensive numerical experiments show that this form of the scaled BFGS method outperforms the standard BFGS method or some similar scaled methods.