A gradient-type algorithm with backward inertial steps associated to a nonconvex minimization problem

2019 ◽  
Vol 84 (2) ◽  
pp. 485-512 ◽  
Author(s):  
Cristian Daniel Alecsa ◽  
Szilárd Csaba László ◽  
Adrian Viorel
Keyword(s):  
Minimization Problem ◽  
Nonconvex Minimization ◽  
Type Algorithm ◽  
Gradient Type

scholarly journals An efficient three-term conjugate gradient-type algorithm for monotone nonlinear equations

2020 ◽  
Author(s):  
Jamilu Sabi'u ◽  
Abdullah Shah
Keyword(s):  
Global Convergence ◽  
Nonlinear Equations ◽  
Conjugate Gradient ◽  
Large Scale ◽  
Numerical Results ◽  
Search Direction ◽  
Projection Technique ◽  
Type Algorithm ◽  
Gradient Type

In this article, we proposed two Conjugate Gradient (CG) parameters using the modified Dai-{L}iao condition and the descent three-term CG search direction. Both parameters are incorporated with the projection technique for solving large-scale monotone nonlinear equations. Using the Lipschitz and monotone assumptions, the global convergence of methods has been proved. Finally, numerical results are provided to illustrate the robustness of the proposed methods.

scholarly journals A gradient-type algorithm for constrained optimization with application to microstructure optimization

2020 ◽  
Vol 25 (5) ◽  
pp. 1729-1755
Author(s):  
Cristian Barbarosie ◽  
◽  
Anca-Maria Toader ◽  
Sérgio Lopes ◽  
Keyword(s):  
Constrained Optimization ◽  
Type Algorithm ◽  
Gradient Type

scholarly journals A gradient-type algorithm optimizing the coupling between matrices

2008 ◽  
Vol 429 (5-6) ◽  
pp. 1229-1242 ◽  
Author(s):  
Catherine Fraikin ◽  
Yurii Nesterov ◽  
Paul Van Dooren
Keyword(s):  
Type Algorithm ◽  
Gradient Type

Convergence analysis of smoothed stochastic gradient-type algorithm

1987 ◽  
Vol 18 (6) ◽  
pp. 1061-1078 ◽  
Author(s):  
NADAV BERMAN ◽  
ARIE FEUER ◽  
ELIAS WAHNON
Keyword(s):  
Convergence Analysis ◽  
Stochastic Gradient ◽  
Type Algorithm ◽  
Gradient Type

scholarly journals A stochastic gradient type algorithm for closed-loop problems

2007 ◽  
Vol 119 (1) ◽  
pp. 51-78 ◽  
Author(s):  
Kengy Barty ◽  
Jean-Sébastien Roy ◽  
Cyrille Strugarek
Keyword(s):  
Closed Loop ◽  
Stochastic Gradient ◽  
Type Algorithm ◽  
Gradient Type

scholarly journals Shrinking Projection Methods for Accelerating Relaxed Inertial Tseng-Type Algorithm with Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Hasanen A. Hammad ◽  
Habib ur Rehman ◽  
Manuel De la Sen
Keyword(s):  
Hilbert Space ◽  
Strong Convergence ◽  
Minimization Problem ◽  
Numerical Experiments ◽  
Real Hilbert Space ◽  
Projection Methods ◽  
Novel Structure ◽  
Convergence Results ◽  
Type Algorithm ◽  
Shrinking Projection Methods

Our main goal in this manuscript is to accelerate the relaxed inertial Tseng-type (RITT) algorithm by adding a shrinking projection (SP) term to the algorithm. Hence, strong convergence results were obtained in a real Hilbert space (RHS). A novel structure was used to solve an inclusion and a minimization problem under proper hypotheses. Finally, numerical experiments to elucidate the applications, performance, quickness, and effectiveness of our procedure are discussed.

scholarly journals Stability of differential inclusions: A computational approach

2006 ◽  
Vol 2006 ◽  
pp. 1-15 ◽  
Author(s):  
Vadim Azhmyakov
Keyword(s):  
Asymptotic Stability ◽  
Lyapunov Functions ◽  
Differential Inclusions ◽  
Auxiliary Problem ◽  
Saddle Points ◽  
Computational Approach ◽  
Saddle Point Problems ◽  
Difference Inclusions ◽  
Type Algorithm ◽  
Gradient Type

We present a technique for analysis of asymptotic stability for a class of differential inclusions. This technique is based on the Lyapunov-type theorems. The construction of the Lyapunov functions for differential inclusions is reduced to an auxiliary problem of mathematical programming, namely, to the problem of searching saddle points of a suitable function. The computational approach to the auxiliary problem contains a gradient-type algorithm for saddle-point problems. We also extend our main results to systems described by difference inclusions. The obtained numerical schemes are applied to some illustrative examples.

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