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

Class HomogeneousPathFollowingMinimizer

java.lang.Object

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

All Implemented Interfaces:

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

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

This implementation solves a Semi-Definite Programming problem using the Homogeneous Self-Dual Path-Following algorithm.

See Also:

• "Andreas Antoniou, Wu-Sheng Lu, "Algorithm 14.1, Primal-dual path-following algorithm," Practical Optimization: Algorithms and Engineering Applications."
• "K. C. Toh, M. J. Todd, R. H. Tütüncü, "SDPT3 -- a MATLAB software package for semidefinite programming, version 2.1," OPTIMIZATION METHODS AND SOFTWARE, 1999."

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
class	HomogeneousPathFollowingMinimizer.Solution	This is the solution to a Semi-Definite Programming problem using the Homogeneous Self-Dual Path-Following algorithm.

Constructor Summary

Constructors

Constructor	Description
HomogeneousPathFollowingMinimizer(double epsilon)	Constructs a Homogeneous Self-Dual Path-Following minimizer to solve semi-definite programming problems.
HomogeneousPathFollowingMinimizer(double gamma0, double sigma0, double epsilon)	Constructs a Homogeneous Self-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.
HomogeneousPathFollowingMinimizer.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

HomogeneousPathFollowingMinimizer

public HomogeneousPathFollowingMinimizer(double gamma0,
                                         double sigma0,
                                         double epsilon)

Constructs a Homogeneous Self-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.

sigma0 - \(0 \leq \sigma < 1\), the centering parameter

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

HomogeneousPathFollowingMinimizer

public HomogeneousPathFollowingMinimizer(double epsilon)

Constructs a Homogeneous Self-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 HomogeneousPathFollowingMinimizer.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