Duality and saddle-point type optimality for interval-valued programming

2013 ◽  
Vol 8 (3) ◽  
pp. 1077-1091 ◽  
Author(s):  
Yuhua Sun ◽  
Xiumei Xu ◽  
Laisheng Wang
Keyword(s):  
Saddle Point ◽  
Point Type ◽  
Interval Valued

scholarly journals A saddle point type solution for a system of operator equations

2021 ◽  
pp. 1-12
Author(s):  
Piotr Kowalski
Keyword(s):  
Saddle Point ◽  
Minimax Theorem ◽  
Dirichlet Problems ◽  
Type Solution ◽  
Operator Equations ◽  
Potential Operators ◽  
System Of Operator Equations ◽  
Ky Fan ◽  
Point Type

Let Ω⊂Rn n>1 and let p,q≥2. We consider the system of nonlinear Dirichlet problems equation* brace(Au)(x)=Nu′(x,u(x),v(x)),x∈Ω,r-(Bv)(x)=Nv′(x,u(x),v(x)),x∈Ω,ru(x)=0,x∈∂Ω,rv(x)=0,x∈∂Ω,endequation* where N:R×R→R is C1 and is partially convex-concave and A:W01,p(Ω)→(W01,p(Ω))* B:W01,p(Ω)→(W01,p(Ω))* are monotone and potential operators. The solvability of this system is reached via the Ky–Fan minimax theorem.

scholarly journals New Preconditioners for Nonsymmetric Saddle Point Systems with Singular (1,1) Block

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Qingbing Liu
Keyword(s):  
Saddle Point ◽  
Krylov Subspace ◽  
Optimal Parameter ◽  
Spectral Characteristics ◽  
Ill Conditioning ◽  
Preconditioned Iterative ◽  
Preconditioned Iterative Methods ◽  
Saddle Point Matrix ◽  
Large Linear Systems ◽  
Point Type

We investigate the solution of large linear systems of saddle point type with singular (1,1) block by preconditioned iterative methods and consider two parameterized block triangular preconditioners used with Krylov subspace methods which have the attractive property of improved eigenvalue clustering with increased ill-conditioning of the (1,1) block of the saddle point matrix, including the choice of the parameter. Meanwhile, we analyze the spectral characteristics of two preconditioners and give the optimal parameter in practice. Numerical experiments that validate the analysis are presented.

Multigrid relaxation methods for systems of saddle point type

2008 ◽  
Vol 58 (12) ◽  
pp. 1933-1950 ◽  
Author(s):  
C.W. Oosterlee ◽  
F.J. Gaspar
Keyword(s):  
Saddle Point ◽  
Relaxation Methods ◽  
Point Type
Sign in / Sign up

Export Citation Format

Share Document