SuanShu, a Java numerical and statistical library

com.numericalmethod.suanshu.optimization.multivariate.constrained.convex.sdp.problem

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}
"Andreas Antoniou, Wu-Sheng Lu, "Section 14.2, Primal and Dual SDP Problems," Practical Optimization: Algorithms and Engineering Applications."
• Nested Class Summary

Nested Classes
Modifier and Type Class and 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 and Description
SDPDualProblem(Vector b, SymmetricMatrix C, SymmetricMatrix[] A)
Constructs a dual SDP problem.
• Method Summary

All Methods
Modifier and Type Method and 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 com.numericalmethod.suanshu.optimization.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