dualalg.c File Reference

Implements the dual-scaling algorithm. More...

Go to the source code of this file.

Functions
int	DSDPChooseBarrierParameter (DSDP, double, double *, double *)
	DSDP barrier heuristic choses the smalles value of mu such that X>0. More...
int	DSDPComputeAndFactorS (DSDP dsdp, DSDPTruth *psdefinite)
	Compute and factor the dual matrix variables. More...
int	DSDPComputeDualStepDirections (DSDP dsdp)
	Compute the step direction by computing a linear system and solving it. More...
int	DSDPInitializeVariables (DSDP dsdp)
	Initialize variables and factor S. More...
int	DSDPResetY0 (DSDP)
	After 1 iteration, consider increasing the variable r. More...
int	DSDPSolveDynamicRho (DSDP dsdp)
	Apply dual-scaling algorithm. More...
int	DSDPYStepLineSearch (DSDP, double, double, DSDPVec)
	Used for Newton step, the merit function of this line search is the dual potential function. More...
int	DSDPYStepLineSearch2 (DSDP, double, double, DSDPVec)
	Used for centering steps, the merit function of this line search is the objective function plus the barrier term. More...

Detailed Description

Implements the dual-scaling algorithm.

Definition in file dualalg.c.

Function Documentation

DSDPChooseBarrierParameter()

int DSDPChooseBarrierParameter	(	DSDP	dsdp,
		double	mutarget,
		double *	ppstep,
		double *	nextmutarget
	)

DSDP barrier heuristic choses the smalles value of mu such that X>0.

Parameters

dsdp	solver
mutarget	current barrier parameter
ppstep	set to primal step length
nextmutarget	set to new target barrier parameter

This routine implements a dynamic strategy for reducing the barrier parameter. Basically, it looks for the smallest barrier parameter for which the primal matrix X is psd. Lower and upper bounds to this parameter also apply.

Definition at line 240 of file dualalg.c.

DSDPComputeDualStepDirections()

int DSDPComputeDualStepDirections

(

DSDP

dsdp

)

Compute the step direction by computing a linear system and solving it.

Parameters

dsdp	the solver

DSDP first attempts unpreconditioned CG to the matrix. Once the number of iterations becomes too large, it swithes a CG preconditioned by the Cholesky factorization. Usually only one iteration of the preconditioned CG is necessary, but solutions with large norms and very precise solutions may require additional iterations.

Definition at line 370 of file dualalg.c.

DSDPInitializeVariables()

int DSDPInitializeVariables

(

DSDP

dsdp

)

Initialize variables and factor S.

Parameters

dsdp	the solver

Definition at line 475 of file dualalg.c.

DSDPResetY0()

int DSDPResetY0

(

DSDP

dsdp

)

After 1 iteration, consider increasing the variable r.

Parameters

dsdp

solver

Definition at line 328 of file dualalg.c.

DSDPSolveDynamicRho()

int DSDPSolveDynamicRho

(

DSDP

dsdp

)

Apply dual-scaling algorithm.

Parameters

dsdp	the solver

Definition at line 121 of file dualalg.c.

DSDPYStepLineSearch()

int DSDPYStepLineSearch	(	DSDP	dsdp,
		double	mutarget,
		double	dstep0,
		DSDPVec	dy
	)

Used for Newton step, the merit function of this line search is the dual potential function.

Parameters

dsdp	the solver
mutarget	barrier parameter
dstep0	initial step length
dy	step direction

Definition at line 24 of file dualalg.c.

DSDPYStepLineSearch2()

int DSDPYStepLineSearch2	(	DSDP	dsdp,
		double	mutarget,
		double	dstep0,
		DSDPVec	dy
	)

Used for centering steps, the merit function of this line search is the objective function plus the barrier term.

Parameters

dsdp	the solver
mutarget	barrier parameter
dstep0	initial step length
dy	step direction

Definition at line 73 of file dualalg.c.