[petsc-users] Extending PETSC-SNES-VI to linear inequality constraints,

[subramanya sadasiva]

Hi Jed, I was just looking through the SNES documentation, I came  across SNESLineSearchSetVIFunctions. Is there an example of the use of this function to implement and arbitrary projection?  Can I use this to implement a function that projects the solution back into the feasible region? I am assuming this should be able to handle simple linear inequality constraints of the type that I have, which can be applied pointwise. Thanks, Subramanya. 

From: potaman at outlook.com
To: jedbrown at mcs.anl.gov; petsc-users at mcs.anl.gov
Date: Mon, 23 Dec 2013 23:34:53 -0500
Subject: Re: [petsc-users] Extending PETSC-SNES-VI to linear inequality constraints, 




I am trying to solve a multiphase cahn hilliard equation with an obstacle potential. So I have an energy functional. However, the linear inequality arises when I eliminate one of the phase variables.  So, the variables are phi1,phi2, phi3 , mu1,mu2 and mu3.  with ,0<phi1,phi2,phi3<1 and phi1+phi2+phi3 =1 . If I get rid of phi3 and mu3, I get an additional constraint 0 < phi1+phi2 < 1 , which I just added to the lagrangian with a multiplier.  

> From: jedbrown at mcs.anl.gov
> To: potaman at outlook.com; petsc-users at mcs.anl.gov
> CC: tmunson at mcs.anl.gov
> Subject: Re: [petsc-users] Extending PETSC-SNES-VI to linear inequality constraints,
> Date: Mon, 23 Dec 2013 21:27:57 -0700
> 
> subramanya sadasiva <potaman at outlook.com> writes:
> 
> > Hi, Is it possible to extend PETSC-SNES VI to handlie linear
> > inequality constraints. My problem has 4 variables . 2 of them have
> > bounds constraints, as well as a linear inequality. At present I've
> > implemented an augmented lagrangian method to handle the linear
> > inequality and I let SNES VI handle the bounds constraints. However,
> > the convergence of this method is very poor. I'd like to know if there
> > was an easy way to get SNES VI to handle the linear inequalities as
> > well. Thanks,
> 
> This would be a useful extension, though I think nonlinear inequality
> constraints may ultimately be necessary.  We are integrating TAO as a
> module in PETSc, which will help with problem formulation.
> 
> Does your problem have an "energy" or objective functional, or is it a
> general variational inequality?
 		 	   		   		 	   		  
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