SDPDualProblem (NM DEV API (v1.2.4) by NM)

java.lang.Object
- dev.nm.solver.multivariate.constrained.problem.ConstrainedOptimProblemImpl1
- - dev.nm.solver.multivariate.constrained.convex.sdp.problem.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 Instance Methods Concrete Methods
Modifier and Type	Method	Description
`SymmetricMatrix`	`A(int i)`	Gets A_i.
`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 A_i.
    
    Parameters:
    
    i - an index to the A's, counting from 1
    
    Returns:
    
    A_i