dualalg.c File Reference

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Detailed Description

Implements the dual-scaling algorithm.

Definition in file dualalg.c.

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.
int	DSDPComputeAndFactorS (DSDP dsdp, DSDPTruth *psdefinite)
	Compute and factor the dual matrix variables.
int	DSDPComputeDualStepDirections (DSDP dsdp)
	Compute the step direction by computing a linear system and solving it.
int	DSDPInitializeVariables (DSDP dsdp)
	Initialize variables and factor S.
int	DSDPResetY0 (DSDP)
	After 1 iteration, consider increasing the variable r.
int	DSDPSolveDynamicRho (DSDP dsdp)
	Apply dual-scaling algorithm.
int	DSDPYStepLineSearch (DSDP, double, double, DSDPVec)
	Used for Newton step, the merit function of this line search is the dual potential function.
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.

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Function Documentation

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.

Referenced by DSDPSolveDynamicRho().

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.

Referenced by DSDPSolveDynamicRho().

int DSDPInitializeVariables

(

DSDP

dsdp

)

Initialize variables and factor S.

Parameters:

dsdp

the solver

Definition at line 475 of file dualalg.c.

Referenced by DSDPSolve().

int DSDPResetY0

(

DSDP

dsdp

)

After 1 iteration, consider increasing the variable r.

Parameters:

dsdp

solver

Definition at line 328 of file dualalg.c.

Referenced by DSDPSolveDynamicRho().

int DSDPSolveDynamicRho

(

DSDP

dsdp

)

Apply dual-scaling algorithm.

Parameters:

dsdp

the solver

Definition at line 121 of file dualalg.c.

Referenced by DSDPSolve().

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.

Referenced by DSDPSolveDynamicRho().

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.

Referenced by DSDPSolveDynamicRho().