dev.nm.solver.multivariate.constrained.convex.sdp.socp.interiorpoint

Class PrimalDualInteriorPointMinimizer1

java.lang.Object

dev.nm.solver.multivariate.constrained.convex.sdp.socp.interiorpoint.PrimalDualInteriorPointMinimizer1

All Implemented Interfaces:

Minimizer<SOCPDualProblem1,IterativeSolution<PrimalDualSolution>>, ConstrainedMinimizer<SOCPDualProblem1,IterativeSolution<PrimalDualSolution>>, Optimizer<SOCPDualProblem1,IterativeSolution<PrimalDualSolution>>

public class PrimalDualInteriorPointMinimizer1
extends Object
implements ConstrainedMinimizer<SOCPDualProblem1,IterativeSolution<PrimalDualSolution>>

The SOCP dual problem we are solving here is : \max {\bm b}^T \hat{\bm y} \\ {\rm s.t.} ({\bm A_i^q})^T \hat{\bm y} + {\bm z_i^q} = c_i^q，\ {\bm z_i^q}\in \mathcal{K}_q^{q_i},\ for i\in [n_q];\\ ({\bm A^{\ell}})^T \hat{\bm y} + {\bm z}^{\ell} = c^{\ell}，\ {\bm z}^{\ell} \ge 0;\\ ({\bm A^u})^T \hat{\bm y} = c^u;\\ \hat{\bm y} \in \mathbb{R}^m;\ {\bm z}^{\ell}\in \mathbb{R}^{n_{\ell}};\ {\bm z}^u \in \mathbb{R}^{n_u}. We implement Primal-Dual Predictor-Corrector Interior Point Method to solve it. Reference: "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	PrimalDualInteriorPointMinimizer1.Solution This is the solution to a Dual Second-Order Conic Programming problem using the Primal-Dual Predictor-Corrector Interior Point algorithm.

Constructor Summary

Constructors

Constructor and Description
PrimalDualInteriorPointMinimizer1(double epsilon, int maxIterations) Constructs a Primal Dual Interior Point minimizer to solve Dual Second Order Conic Programming problems.

Method Summary

Modifier and Type	Method and Description
PrimalDualInteriorPointMinimizer1.Solution	solve(SOCPDualProblem1 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

PrimalDualInteriorPointMinimizer1

public PrimalDualInteriorPointMinimizer1(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 PrimalDualInteriorPointMinimizer1.Solution solve(SOCPDualProblem1 problem)
                                                 throws Exception

Description copied from interface: Optimizer

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

Specified by:

solve in interface Optimizer<SOCPDualProblem1,IterativeSolution<PrimalDualSolution>>

Parameters:

problem - an optimization problem

Returns:

a solution to the optimization problem

Throws:

Exception - when there is an error solving the problem