# SuanShu, a Java numerical and statistical library

com.numericalmethod.suanshu.optimization.multivariate.constrained.convex.sdp.socp.interiorpoint

## Class PrimalDualInteriorPointMinimizer

• java.lang.Object
• com.numericalmethod.suanshu.optimization.multivariate.constrained.convex.sdp.socp.interiorpoint.PrimalDualInteriorPointMinimizer
• All Implemented Interfaces:
Minimizer<SOCPDualProblem,IterativeSolution<PrimalDualSolution>>, ConstrainedMinimizer<SOCPDualProblem,IterativeSolution<PrimalDualSolution>>, Optimizer<SOCPDualProblem,IterativeSolution<PrimalDualSolution>>

public class PrimalDualInteriorPointMinimizer
extends Object
implements ConstrainedMinimizer<SOCPDualProblem,IterativeSolution<PrimalDualSolution>>
Solves a Dual Second Order Conic Programming problem using the Primal Dual Interior Point algorithm. The dual problem is of the form: $\max_y \mathbf{b'y} \textrm{ s.t.,} \\ \mathbf{\hat{A}_i'y + s_i = \hat{c}_i} \\ s_i \in K_i, i = 1, 2, ..., q$

• "Andreas Antoniou, Wu-Sheng Lu, "Algorithm 14.5, Section 14.8.2, A primal-dual interior-point algorithm," Practical Optimization: Algorithms and Engineering Applications."
• "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 and Description
class  PrimalDualInteriorPointMinimizer.Solution
This is the solution to a Dual Second Order Conic Programming problem using the Primal Dual Interior Point algorithm.
• ### Constructor Summary

Constructors
Constructor and Description
PrimalDualInteriorPointMinimizer(double epsilon, int maxIterations)
Constructs a Primal Dual Interior Point minimizer to solve Dual Second Order Conic Programming problems.
• ### Method Summary

All Methods
Modifier and Type Method and Description
PrimalDualInteriorPointMinimizer.Solution solve(SOCPDualProblem 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

• #### PrimalDualInteriorPointMinimizer

public PrimalDualInteriorPointMinimizer(double epsilon,
int maxIterations)
Constructs a Primal Dual Interior Point minimizer to solve Dual Second Order Conic Programming problems.
Parameters:
epsilon - a precision parameter: when a number |x| ≤ ε, it is considered 0
maxIterations - the maximum number of iterations
• ### Method Detail

• #### solve

public PrimalDualInteriorPointMinimizer.Solution solve(SOCPDualProblem problem)
throws Exception
Description copied from interface: Optimizer
Solve an optimization problem, e.g., OptimProblem.
Specified by:
solve in interface Optimizer<SOCPDualProblem,IterativeSolution<PrimalDualSolution>>
Parameters:
problem - an optimization problem
Returns:
a solution to the optimization problem
Throws:
Exception - when there is an error solving the problem