dev.nm.solver.multivariate.constrained.convex.sdp.problem

Class SDPPrimalProblem

java.lang.Object

dev.nm.solver.multivariate.constrained.convex.sdp.problem.SDPPrimalProblem

public class SDPPrimalProblem
extends Object

A Primal SDP problem, as in equation 14.1 in the reference, takes the following form. \[ \begin{aligned} & \underset{X}{\text{minimize}} & & \mathbf{C \cdot X} \\ & \text{subject to} & & \mathbf{A_i \cdot X} = \mathbf{b_i} \text{ for } i = 1, 2, ..., p \\ &&& \mathbf{X} \succeq \mathbf{0} \end{aligned} \]

See Also:

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

Constructor Summary

Constructors

Constructor and Description
SDPPrimalProblem(SymmetricMatrix C, SymmetricMatrix[] A) Constructs a primal SDP problem. \[ \min_x \mathbf{c'x} \textrm{, s.t., } \\ \mathbf{Ax} = \mathbf{b}, \mathbf{x} \geq \mathbf{0} \]

Method Summary

Modifier and Type	Method and Description
SymmetricMatrix	A(int i) Gets \(A_{i}\).
SymmetricMatrix	C() Gets C.
int	n() Gets the dimension of the system, i.e., the dimension of x, the number of variables.
int	p() Gets the size of b.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

SDPPrimalProblem

public SDPPrimalProblem(SymmetricMatrix C,
                        SymmetricMatrix[] A)

Constructs a primal SDP problem. \[ \min_x \mathbf{c'x} \textrm{, s.t., } \\ \mathbf{Ax} = \mathbf{b}, \mathbf{x} \geq \mathbf{0} \]

Parameters:

C - \(C\)

A - \(A\)

Method Detail

n

public int n()

Gets the dimension of the system, i.e., the dimension of x, the number of variables.

Returns:

the dimension of the system

p

public int p()

Gets the size of b.

Returns:

the size of 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:

\(A_{i}\)