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

Class SOCPGeneralProblem1

java.lang.Object

dev.nm.solver.multivariate.constrained.convex.sdp.socp.problem.SOCPDualProblem1

dev.nm.solver.multivariate.constrained.convex.sdp.socp.problem.SOCPGeneralProblem1

All Implemented Interfaces:

ConstrainedOptimProblem, OptimProblem

Direct Known Subclasses:

SOCPPortfolioProblem1

public class SOCPGeneralProblem1
extends SOCPDualProblem1

Many convex programming problems can be represented in the following form. \[ \begin{align*} \min_x \quad & \mathbf{f^T} x \\ \textrm{s.t.} \quad & \lVert {A_i}^T x + c_i \rVert_2 \leq b_i^T x + d_i,\quad i = 1,\dots,m \end{align*} \] where the problem parameters are \[ x\in\mathbb{R}^n, f \in \mathbb{R}^n, \ A_i \in \mathbb{R}^{{n_i}\times n}, \ c_i \in \mathbb{R}^{n_i}, \ b_i \in \mathbb{R}^n, \ d_i \in \mathbb{R} \]

Note: This class extends SOCPDualProblem with \(x = -y\): \[ \begin{align*} \max_y \quad & \mathbf{b^T y} \\ \textrm{s.t.} \quad & \mathbf{\hat{A}^T_i y + s_i = \hat{c}_i} \\ & s_i \in \mathcal{K}_i,\quad i = 1, 2, ..., q \end{align*} \] where \[ \hat{A}^T_i = \begin{bmatrix} b^T_i\\ A^T_i \end{bmatrix}, \hat{c}_i = \begin{bmatrix} d_i\\ c_i \end{bmatrix} \] and each \(\mathcal{K}_i\) denotes a second order cone with \[ \mathcal{K}_i \triangleq \left \{ s_i = \begin{bmatrix} s^0_i \\ \bar{s_i} \end{bmatrix} \in \mathbb{R}^n : s^0_i \geq \left \| \bar{s_i} \right \|_2, s_i^0 \in \mathbb{R},\ \bar{s_i} \in \mathbb{R}^{n-1} \right \} \] If an instance of this class is passed to a dual problem solver, e.g., PrimalDualInteriorPointMinimizer, the solution to the original problem is \(-y\) in the returned PrimalDualSolution.

See Also:

• Wikipedia: Second-order cone programming
• "Andreas Antoniou, Wu-Sheng Lu, "eq 14.104, Section 14.7, Second-Order Cone Programming," Practical Optimization: Algorithms and Engineering Applications."

Nested Class Summary

Nested classes/interfaces inherited from class dev.nm.solver.multivariate.constrained.convex.sdp.socp.problem.SOCPDualProblem1

SOCPDualProblem1.EqualityConstraints

Constructor Summary

Constructors

Constructor and Description
SOCPGeneralProblem1(SOCPGeneralProblem1 that) Copy constructor.
SOCPGeneralProblem1(Vector f, List<SOCPGeneralConstraint> generalConstraints) Construct a general Second Order Conic Programming problem. \[ \begin{align*} \min_x \quad & \mathbf{f^T} x \\ \textrm{s.t.}
SOCPGeneralProblem1(Vector f, List<SOCPGeneralConstraint> generalConstraints, List<SOCPLinearInequality> linearInequalities, List<SOCPLinearEquality> linearEqualities) Construct a general Second Order Conic Programming problem. \[ \begin{align*} \min_x \quad & \mathbf{f^T} x \\ \textrm{s.t.}
SOCPGeneralProblem1(Vector f, SOCPGeneralConstraint[] generalConstraints, SOCPLinearInequality[] linearInequalities, SOCPLinearEquality[] linearEqualities) Construct a general Second Order Conic Programming problem.\[ \begin{align*} \min_x \quad &; \mathbf{f^T} x \\ \textrm{s.t.}

Method Summary

Methods inherited from class dev.nm.solver.multivariate.constrained.convex.sdp.socp.problem.SOCPDualProblem1

A_full, A_l_full, A_l, A_q_full, A_q, A_u, b, c_full, c_l_full, c_l, c_q_full, c_q, c_u, dimension, f, flag_s, flag_u, getEqualityConstraints, getLessThanConstraints, m, n_l, n_q, n_u, n

Methods inherited from class java.lang.Object

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

Constructor Detail

SOCPGeneralProblem1

public SOCPGeneralProblem1(Vector f,
                           List<SOCPGeneralConstraint> generalConstraints)

Construct a general Second Order Conic Programming problem. \[ \begin{align*} \min_x \quad & \mathbf{f^T} x \\ \textrm{s.t.} \quad & \lVert {A_i}^T x + c_i \rVert_2 \leq b_i^T x + d_i,\quad i = 1,\dots,m \end{align*} \]

Parameters:

f - f

generalConstraints - the SOCP constraints

SOCPGeneralProblem1

public SOCPGeneralProblem1(Vector f,
                           List<SOCPGeneralConstraint> generalConstraints,
                           List<SOCPLinearInequality> linearInequalities,
                           List<SOCPLinearEquality> linearEqualities)

Construct a general Second Order Conic Programming problem. \[ \begin{align*} \min_x \quad & \mathbf{f^T} x \\ \textrm{s.t.} \quad & \lVert {A_i}^T x + c_i \rVert_2 \leq b_i^T x + d_i,\quad i = 1,\dots,m \end{align*} \]

Parameters:

f - f

generalConstraints - the SOCP constraints

linearInequalities - the linear inequalities

linearEqualities - the linear equalities

SOCPGeneralProblem1

public SOCPGeneralProblem1(Vector f,
                           SOCPGeneralConstraint[] generalConstraints,
                           SOCPLinearInequality[] linearInequalities,
                           SOCPLinearEquality[] linearEqualities)

Construct a general Second Order Conic Programming problem.\[ \begin{align*} \min_x \quad &; \mathbf{f^T} x \\ \textrm{s.t.} \quad &; \lVert {A_i}^T x + c_i \rVert_2 \leq b_i^T x + d_i,\quad i = 1,\dots,m \end{align*} \]

Parameters:

f - f

generalConstraints - the SOCP constraints

linearInequalities - the linear inequalities

linearEqualities - the linear equalities

SOCPGeneralProblem1

public SOCPGeneralProblem1(SOCPGeneralProblem1 that)

Copy constructor.

Parameters:

that - another SOCPGeneralProblem