## Class SDPDualProblem

• 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}
• ### Nested Class Summary

Nested Classes
Modifier and Type Class Description
static class  SDPDualProblem.EqualityConstraints
This is the collection of equality constraints: $\sum_{i=1}^{p}y_i\mathbf{A_i}+\textbf{S} = \textbf{C}, \textbf{S} \succeq \textbf{0}$
• ### Constructor Summary

Constructors
Constructor Description
SDPDualProblem​(Vector b, SymmetricMatrix C, SymmetricMatrix[] A)
Constructs a dual SDP problem.
• ### Method Summary

All Methods
Modifier and Type Method Description
SymmetricMatrix A​(int i)
Gets Ai.
ImmutableVector b()
Gets b.
SymmetricMatrix C()
Gets C.
int n()
Gets the dimension of the square matrices C and As.
int p()
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
• ### Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
• ### Constructor Detail

• #### SDPDualProblem

public SDPDualProblem​(Vector b,
SymmetricMatrix C,
SymmetricMatrix[] A)
Constructs a dual SDP problem.
Parameters:
b - $$b$$
C - $$C$$
A - $$A$$
• ### Method Detail

• #### n

public int n()
Gets the dimension of the square matrices C and As.
Returns:
the dimension of the matrices
• #### 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
• #### b

public ImmutableVector b()
Gets b.
Returns:
b
• #### C

public SymmetricMatrix C()
Gets C.
Returns:
C
• #### A

public SymmetricMatrix A​(int i)
Gets Ai.
Parameters:
i - an index to the A's, counting from 1
Returns:
Ai