Class PrimalDualInteriorPointMinimizer1
- java.lang.Object
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- dev.nm.solver.multivariate.constrained.convex.sdp.socp.interiorpoint.PrimalDualInteriorPointMinimizer1
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- 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."
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Nested Class Summary
Nested Classes Modifier and Type Class 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.
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Constructor Summary
Constructors Constructor Description PrimalDualInteriorPointMinimizer1(double epsilon, int maxIterations)
Constructs a Primal Dual Interior Point minimizer to solve Dual Second Order Conic Programming problems.
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description PrimalDualInteriorPointMinimizer1.Solution
solve(SOCPDualProblem1 problem)
Solve an optimization problem, e.g.,OptimProblem
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Constructor Detail
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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 0maxIterations
- the maximum number of iterations
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Method Detail
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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 interfaceOptimizer<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
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