Package dev.nm.solver.multivariate.constrained.convex.sdp.pathfollowing

Class CSDPMinimizer

java.lang.Object

dev.nm.solver.multivariate.constrained.convex.sdp.pathfollowing.CSDPMinimizer

All Implemented Interfaces:

Minimizer<SDPDualProblem,IterativeSolution<CentralPath>>, ConstrainedMinimizer<SDPDualProblem,IterativeSolution<CentralPath>>, Optimizer<SDPDualProblem,IterativeSolution<CentralPath>>

public class CSDPMinimizer
extends Object
implements ConstrainedMinimizer<SDPDualProblem,IterativeSolution<CentralPath>>

Implements the CSDP algorithm for semidefinite programming problem with equality constraints.

See Also:

• "Borchers, Brian, "CSDP, a C Library for Semidefinite Programming", Optimization Methods and Software 11(1): 613-623, 1999."
• "K. C. Toh, M. J. Todd, R. H. Tütüncü, "On the implementation and usage of SDPT3 - a MATLAB software package for semidefinite-quadratic-linear programming, version 4.0," in Handbook on Semidefinite, Cone and Polynomial Optimization: Theory, Algorithms, Software and Applications, Anjos, M. and Lasserre, J.B., ED. Springer, 2012, pp. 715--754."

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
class	CSDPMinimizer.Solution

Constructor Summary

Constructors

Constructor	Description
CSDPMinimizer(double epsilon)	Constructs a Primal-Dual Path-Following minimizer to solve semi-definite programming problems.
CSDPMinimizer(double gamma0, double epsilon)	Constructs a Primal-Dual Path-Following minimizer to solve semi-definite programming problems.

Method Summary

Modifier and Type	Method	Description
protected static double	getMinEigenValue(Matrix A, double epsilon)	Gets the minimum of all the eigenvalues of a matrix.
CSDPMinimizer.Solution	solve(SDPDualProblem problem)	Solve an optimization problem, e.g., OptimProblem.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

CSDPMinimizer

public CSDPMinimizer(double gamma0,
                     double epsilon)

Constructs a Primal-Dual Path-Following minimizer to solve semi-definite programming problems.

Parameters:

gamma0 - \(0 < \gamma < 1\); it ensures the next iterates are inside the feasible set; suggested values are between 0.9 and 0.99

epsilon - a precision par a meter: when a number |x| ≤ ε, it is considered 0

CSDPMinimizer

public CSDPMinimizer(double epsilon)

Constructs a Primal-Dual Path-Following minimizer to solve semi-definite programming problems.

Parameters:

epsilon - a precision parameter: when a number |x| ≤ ε, it is considered 0

Method Detail

solve

public CSDPMinimizer.Solution solve(SDPDualProblem problem)
                             throws Exception

Description copied from interface: Optimizer

Solve an optimization problem, e.g., OptimProblem.

Specified by:

solve in interface Optimizer<SDPDualProblem,IterativeSolution<CentralPath>>

Parameters:

problem - an optimization problem

Returns:

a solution to the optimization problem

Throws:

Exception - when there is an error solving the problem

getMinEigenValue

protected static double getMinEigenValue(Matrix A,
                                         double epsilon)

Gets the minimum of all the eigenvalues of a matrix.

Parameters:

A - a matrix

epsilon - a precision parameter: when a number |x| ≤ ε, it is considered 0

Returns:

the minimum of all the eigenvalues of a matrix