Class SDPDualProblem
- java.lang.Object
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- dev.nm.solver.multivariate.constrained.problem.ConstrainedOptimProblemImpl1
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- dev.nm.solver.multivariate.constrained.convex.sdp.problem.SDPDualProblem
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- All Implemented Interfaces:
ConstrainedOptimProblem,OptimProblem
public class SDPDualProblem extends ConstrainedOptimProblemImpl1
A dual SDP problem, as in equation 14.4 in the reference, takes the following form. \[ \begin{aligned} & \underset{y}{\text{maximize}} & & \mathbf{b^T y} \\ & \text{subject to} & & \sum_{i=1}^{p}y_i\mathbf{A_i}+\textbf{S} = \textbf{C} \\ &&& \textbf{S} \succeq \textbf{0} \end{aligned} \]
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Nested Class Summary
Nested Classes Modifier and Type Class Description static classSDPDualProblem.EqualityConstraintsThis is the collection of equality constraints: \[ \sum_{i=1}^{p}y_i\mathbf{A_i}+\textbf{S} = \textbf{C}, \textbf{S} \succeq \textbf{0} \]
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Constructor Summary
Constructors Constructor Description SDPDualProblem(Vector b, SymmetricMatrix C, SymmetricMatrix[] A)Constructs a dual SDP problem.
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description SymmetricMatrixA(int i)Gets Ai.ImmutableVectorb()Gets b.SymmetricMatrixC()Gets C.intn()Gets the dimension of the square matrices C and As.intp()Gets the dimension of the system, i.e., p = the dimension of y, the number of variables.-
Methods inherited from class dev.nm.solver.multivariate.constrained.problem.ConstrainedOptimProblemImpl1
dimension, f, getEqualityConstraints, getLessThanConstraints
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Constructor Detail
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SDPDualProblem
public SDPDualProblem(Vector b, SymmetricMatrix C, SymmetricMatrix[] A)
Constructs a dual SDP problem.- Parameters:
b- \(b\)C- \(C\)A- \(A\)
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Method Detail
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n
public int n()
Gets the dimension of the square matrices C and As.- Returns:
- the dimension of the matrices
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p
public int p()
Gets the dimension of the system, i.e., p = the dimension of y, the number of variables.- Returns:
- the dimension of the system
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b
public ImmutableVector b()
Gets b.- Returns:
- b
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C
public SymmetricMatrix C()
Gets C.- Returns:
- C
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A
public SymmetricMatrix A(int i)
Gets Ai.- Parameters:
i- an index to the A's, counting from 1- Returns:
- Ai
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