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

Class SOCPDualProblem

java.lang.Object

com.numericalmethod.suanshu.optimization.constrained.convex.sdp.socp.problem.SOCPDualProblem

All Implemented Interfaces:

ConstrainedOptimProblem, OptimProblem, java.io.Serializable

Direct Known Subclasses:

SOCPGeneralProblem

public class SOCPDualProblem
extends java.lang.Object
implements ConstrainedOptimProblem

This is the Dual Second Order Conic Programming problem. \[ \max_y \mathbf{b'y} \textrm{ s.t.,} \\ \mathbf{\hat{A}_i'y + s_i = \hat{c}_i} \\ s_i \in K_i, i = 1, 2, ..., q \]

See Also:

"Andreas Antoniou, Wu-Sheng Lu, "eq 14.102, Section 14.7, Second-Order Cone Programming," Practical Optimization: Algorithms and Engineering Applications.", Serialized Form

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	SOCPDualProblem.EqualityConstraints

Constructor Summary

Constructors

Constructor and Description
SOCPDualProblem(Vector b, Matrix[] A, Vector[] c) Construct a dual SODP problem.

Method Summary

Modifier and Type	Method and Description
ImmutableMatrix	A() \[ A = [A_1, A_2, ...
ImmutableMatrix	A(int i) Get Ai.
ImmutableVector	b() Get b.
ImmutableVector	c()
ImmutableVector	c(int i) Get ci.
int	dimension() Get the number of variables.
RealScalarFunction	f() Get the objective function.
SOCPDualProblem.EqualityConstraints	getEqualityConstraints() Get the equality constraints, hi(x) = 0
LessThanConstraints	getLessThanConstraints() Get the less-than-or-equal-to constraints, gi(x) ≤ 0
int	m() Get the dimension of the system, i.e., m = the dimension of y.
int	n(int i) Get the number of columns of Ai.
int	q() Get the number of A matrices.

Methods inherited from class java.lang.Object

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

Constructor Detail

SOCPDualProblem

public SOCPDualProblem(Vector b,
                       Matrix[] A,
                       Vector[] c)

Construct a dual SODP problem. \[ \max_y \mathbf{b'y} \textrm{ s.t.,} \\ \mathbf{\hat{A}_i'y + s_i = \hat{c}_i} \\ s_i \in K_i, i = 1, 2, ..., q \]

Parameters:

b - \(b\)

A - \(A_i\)'s

c - \(c_i\)'s

Method Detail

dimension

public int dimension()

Description copied from interface: OptimProblem

Get the number of variables.

Specified by:

dimension in interface OptimProblem

Returns:

the number of variables.

f

public RealScalarFunction f()

Description copied from interface: OptimProblem

Get the objective function.

Specified by:

f in interface OptimProblem

Returns:

the objective function

getLessThanConstraints

public LessThanConstraints getLessThanConstraints()

Description copied from interface: ConstrainedOptimProblem

Get the less-than-or-equal-to constraints, g_i(x) ≤ 0

Specified by:

getLessThanConstraints in interface ConstrainedOptimProblem

Returns:

the less-than-or-equal-to constraints

getEqualityConstraints

public SOCPDualProblem.EqualityConstraints getEqualityConstraints()

Description copied from interface: ConstrainedOptimProblem

Get the equality constraints, h_i(x) = 0

Specified by:

getEqualityConstraints in interface ConstrainedOptimProblem

Returns:

the equality constraints

m

public int m()

Get the dimension of the system, i.e., m = the dimension of y.

Returns:

the dimension of the system

q

public int q()

Get the number of A matrices.

Returns:

the number of A matrices

b

public ImmutableVector b()

Get b.

Returns:

b

c

public ImmutableVector c(int i)

Get c_i.

Parameters:

i - an index to the c's, counting from 1

Returns:

c_i

A

public ImmutableMatrix A(int i)

Get A_i.

Parameters:

i - an index to the A's, counting from 1

Returns:

A_i

n

public int n(int i)

Get the number of columns of A_i.

Parameters:

i - an index to the A's, counting from 1

Returns:

the number of columns of A_i

A

public ImmutableMatrix A()

\[ A = [A_1, A_2, ... A_q] \]

Returns:

A

See Also:

"Andreas Antoniou, Wu-Sheng Lu, "Section 14.8.1, Assumptions and KKT conditions," Practical Optimization: Algorithms and Engineering Applications."

c

public ImmutableVector c()