scholarly journals Semismooth Newton-type method for bilevel optimization: global convergence and extensive numerical experiments

2021 ◽  
pp. 1-35
Author(s):  
Andreas Fischer ◽  
Alain B. Zemkoho ◽  
Shenglong Zhou
Keyword(s):  
Global Convergence ◽  
Numerical Experiments ◽  
Bilevel Optimization ◽  
Type Method ◽  
Semismooth Newton

A Non-Monotone Line Search Combination Technique for Unconstrained Optimization

2014 ◽  
Vol 8 (1) ◽  
pp. 218-221 ◽  
Author(s):  
Ping Hu ◽  
Zong-yao Wang
Keyword(s):  
Global Convergence ◽  
Unconstrained Optimization ◽  
Numerical Experiments ◽  
Line Search ◽  
Optimization Problems ◽  
Search Algorithm ◽  
New Combination ◽  
Combination Rule ◽  
Combination Technique ◽  
Unconstrained Optimization Problems

We propose a non-monotone line search combination rule for unconstrained optimization problems, the corresponding non-monotone search algorithm is established and its global convergence can be proved. Finally, we use some numerical experiments to illustrate the new combination of non-monotone search algorithm’s effectiveness.

scholarly journals Stabilised explicit Adams-type methods

2021 ◽  
pp. 82-98
Author(s):  
Vasily I. Repnikov ◽  
Boris V. Faleichik ◽  
Andrew V. Moisa
Keyword(s):  
Numerical Experiments ◽  
Step Method ◽  
Type Method ◽  
Constrained Optimisation ◽  
First Order ◽  
Error Constant ◽  
Stability Intervals ◽  
Multi Step Methods ◽  
First Order Methods ◽  
Accuracy And Stability

In this work we present explicit Adams-type multi-step methods with extended stability intervals, which are analogous to the stabilised Chebyshev Runge – Kutta methods. It is proved that for any k ≥ 1 there exists an explicit k-step Adams-type method of order one with stability interval of length 2k. The first order methods have remarkably simple expressions for their coefficients and error constant. A damped modification of these methods is derived. In the general case, to construct a k-step method of order p it is necessary to solve a constrained optimisation problem in which the objective function and p constraints are second degree polynomials in k variables. We calculate higher-order methods up to order six numerically and perform some numerical experiments to confirm the accuracy and stability of the methods.

On modeling column crystallizers and a Hermite predictor–corrector scheme for a system of integro-differential equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Khaldoun El Khaldi ◽  
Nima Rabiei ◽  
Elias G. Saleeby
Keyword(s):  
Numerical Experiments ◽  
Main Part ◽  
Direct Method ◽  
Particle Agglomeration ◽  
Volterra Type ◽  
Type Method ◽  
Method Of Solution ◽  
System Of Integrodifferential Equations ◽  
Predictor Corrector ◽  
A Direct Method

Abstract Multistaged crystallization systems are used in the production of many chemicals. In this article, employing the population balance framework, we develop a model for a column crystallizer where particle agglomeration is a significant growth mechanism. The main part of the model can be reduced to a system of integrodifferential equations (IDEs) of the Volterra type. To solve this system simultaneously, we examine two numerical schemes that yield a direct method of solution and an implicit Runge–Kutta type method. Our numerical experiments show that the extension of a Hermite predictor–corrector method originally advanced in Khanh (1994) for a single IDE is effective in solving our model. The numerical method is presented for a generalization of the model which can be used to study and simulate a number of possible operating profiles of the column.

scholarly journals A New Jacobian-Like Method for the Polyhedral Cone-Constrained Eigenvalue Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-16
Author(s):  
Guo Sun
Keyword(s):  
Global Convergence ◽  
Eigenvalue Problem ◽  
Numerical Experiments ◽  
Quadratic Convergence ◽  
Polyhedral Cone ◽  
System Of Equations ◽  
Local Quadratic Convergence ◽  
Ncp Function

The eigenvalue problem over a polyhedral cone is studied in this paper. Based on the F-B NCP function, we reformulate this problem as a system of equations and propose a Jacobian-like method. The global convergence and local quadratic convergence of the proposed method are established under suitable assumptions. Preliminary numerical experiments for a special polyhedral cone are reported in this paper to show the validity of the proposed method.

scholarly journals On global convergence rate of two acceleration projection algorithms for solving the multiple-sets split feasibility problem

Filomat ◽  
2016 ◽  
Vol 30 (12) ◽  
pp. 3243-3252 ◽  
Author(s):  
Qiao-Li Dong ◽  
Songnian He ◽  
Yanmin Zhao
Keyword(s):  
Global Convergence ◽  
Convergence Rate ◽  
Numerical Experiments ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Projection Algorithms ◽  
Split Feasibility ◽  
Global Convergence Rate

In this paper, we introduce two fast projection algorithms for solving the multiple-sets split feasibility problem (MSFP). Our algorithms accelerate algorithms proposed in [8] and are proved to have a global convergence rate O(1=n2). Preliminary numerical experiments show that these algorithms are practical and promising.

scholarly journals Un algoritmo global con jacobiano suavizado para problemas de complementariedad no lineal

2021 ◽  
Vol 39 (2) ◽  
Author(s):  
Wilmer Sánchez ◽  
Rosana Pérez ◽  
Héctor Martínez
Keyword(s):  
Global Convergence ◽  
Numerical Experiments ◽  
Complementarity Problems ◽  
Convergence Theory ◽  
System Of Equations ◽  
Nonsmooth System ◽  
The One

In this paper, we use the smoothing Jacobian strategy to propose a new algorithm for solving complementarity problems based on its reformulation as a nonsmooth system of equations. This algorithm can be seen as a generalization of the one proposed in [18]. We develop its global convergence theory and under certain assumptions, we demonstrate that the proposed algorithm converges locally and, q-superlinearly or q-quadratically to a solution of the problem. Some numerical experiments show a good performance of this algorithm.

scholarly journals The Bessel Expansion of Fourier Integral on Finite Interval

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 607
Author(s):  
Yongxiong Zhou ◽  
Zhenyu Zhao
Keyword(s):  
Bessel Function ◽  
Numerical Experiments ◽  
Complex Analysis ◽  
Finite Interval ◽  
Fourier Integral ◽  
Type Method ◽  
Function Expansion ◽  
Oscillation Frequencies

In this paper, we further extend the Filon-type method to the Bessel function expansion for calculating Fourier integral. By means of complex analysis, this expansion is effective for all the oscillation frequencies. Namely, the errors of the expansion not only decrease as the order of the derivative increases, but also decrease rapidly as the frequency increases. Some numerical experiments are also presented to verify the effectiveness of the method.

scholarly journals A General Inertial Viscosity Type Method for Nonexpansive Mappings and Its Applications in Signal Processing

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 288 ◽  
Author(s):  
Yinglin Luo ◽  
Meijuan Shang ◽  
Bing Tan
Keyword(s):  
Signal Processing ◽  
Strong Convergence ◽  
Fixed Points ◽  
Hilbert Spaces ◽  
Numerical Experiments ◽  
Nonexpansive Mappings ◽  
Type Method ◽  
Pseudocontractive Mappings ◽  
Inertia Parameters ◽  
Strictly Pseudocontractive Mappings

In this paper, we propose viscosity algorithms with two different inertia parameters for solving fixed points of nonexpansive and strictly pseudocontractive mappings. Strong convergence theorems are obtained in Hilbert spaces and the applications to the signal processing are considered. Moreover, some numerical experiments of proposed algorithms and comparisons with existing algorithms are given to the demonstration of the efficiency of the proposed algorithms. The numerical results show that our algorithms are superior to some related algorithms.

scholarly journals A Filter Algorithm with Inexact Line Search

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Meiling Liu ◽  
Xueqian Li ◽  
Qinmin Wu
Keyword(s):  
Nonlinear Programming ◽  
Global Convergence ◽  
Local Convergence ◽  
Numerical Experiments ◽  
Line Search ◽  
Second Order ◽  
Lagrangian Function ◽  
Order Correction ◽  
Inexact Line Search ◽  
Mild Conditions

A filter algorithm with inexact line search is proposed for solving nonlinear programming problems. The filter is constructed by employing the norm of the gradient of the Lagrangian function to the infeasibility measure. Transition to superlinear local convergence is showed for the proposed filter algorithm without second-order correction. Under mild conditions, the global convergence can also be derived. Numerical experiments show the efficiency of the algorithm.

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