com.numericalmethod.suanshu.optimization.constrained.convex.sdp.pathfollowing

Class HomogeneousPathFollowing

java.lang.Object

com.numericalmethod.suanshu.optimization.constrained.convex.sdp.pathfollowing.HomogeneousPathFollowing

All Implemented Interfaces:

ConstrainedMinimizer<SDPDualProblem,IterativeMinimizer<CentralPath>>, Minimizer<SDPDualProblem,IterativeMinimizer<CentralPath>>, Optimizer<SDPDualProblem,IterativeMinimizer<CentralPath>>, java.io.Serializable

public class HomogeneousPathFollowing
extends java.lang.Object
implements ConstrainedMinimizer<SDPDualProblem,IterativeMinimizer<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."

, Serialized Form

Nested Class Summary

Nested Classes

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

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method and Description
HomogeneousPathFollowing.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

HomogeneousPathFollowing

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

Construct 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

HomogeneousPathFollowing

public HomogeneousPathFollowing(double epsilon)

Construct 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 HomogeneousPathFollowing.Solution solve(SDPDualProblem problem)
                                        throws java.lang.Exception

Description copied from interface: Optimizer

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

Specified by:

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

Parameters:

problem - an optimization problem

Returns:

a solution to the optimization problem

Throws:

java.lang.Exception - when there is an error solving the problem