Class SOCPGeneralProblem
- java.lang.Object
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- dev.nm.solver.multivariate.constrained.convex.sdp.socp.problem.SOCPDualProblem
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- dev.nm.solver.multivariate.constrained.convex.sdp.socp.problem.SOCPGeneralProblem
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- All Implemented Interfaces:
ConstrainedOptimProblem
,OptimProblem
- Direct Known Subclasses:
SOCPPortfolioProblem
public class SOCPGeneralProblem extends SOCPDualProblem
Many convex programming problems can be represented in the following form. Minimize \[ f^' x \] subject to \[ \lVert A_i x + b_i \rVert_2 \leq c_i^T x + d_i,\quad i = 1,\dots,m \] where the problem parameters are \[ x\in\mathbb{R}^n, f \in \mathbb{R}^n, \ A_i \in \mathbb{R}^{{n_i}\times n}, \ b_i \in \mathbb{R}^{n_i}, \ c_i \in \mathbb{R}^n, \ d_i \in \mathbb{R} \] Note: This class extends SOCPDualProblem with x = -y: \[ \max_y \mathbf{b'y} \textrm{ s.t.,} \\ \mathbf{\hat{A}_i'y + s_i = \hat{c}_i} \\ s_i \in K_i, i = 1, 2, ..., q \] 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."
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Nested Class Summary
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Nested classes/interfaces inherited from class dev.nm.solver.multivariate.constrained.convex.sdp.socp.problem.SOCPDualProblem
SOCPDualProblem.EqualityConstraints
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Constructor Summary
Constructors Constructor Description SOCPGeneralProblem(Vector f, SOCPGeneralConstraint[] constraints)
Construct a general Second Order Conic Programming problem.SOCPGeneralProblem(Vector f, List<SOCPGeneralConstraint> constraints)
Construct a general Second Order Conic Programming problem.SOCPGeneralProblem(SOCPGeneralProblem that)
Copy constructor.
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Method Summary
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Methods inherited from class dev.nm.solver.multivariate.constrained.convex.sdp.socp.problem.SOCPDualProblem
A, A, b, c, c, dimension, f, getEqualityConstraints, getLessThanConstraints, m, n, q
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Constructor Detail
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SOCPGeneralProblem
public SOCPGeneralProblem(SOCPGeneralProblem that)
Copy constructor.- Parameters:
that
- another SOCPGeneralProblem
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SOCPGeneralProblem
public SOCPGeneralProblem(Vector f, SOCPGeneralConstraint[] constraints)
Construct a general Second Order Conic Programming problem. Minimize \[ f^' x \] subject to the SOCP constraints \[ \lVert A_i x + b_i \rVert_2 \leq c_i^T x + d_i,\quad i = 1,\dots,m \]- Parameters:
f
- fconstraints
- the SOCP constraints
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SOCPGeneralProblem
public SOCPGeneralProblem(Vector f, List<SOCPGeneralConstraint> constraints)
Construct a general Second Order Conic Programming problem. Minimize \[ f^' x \] subject to the SOCP constraints \[ \lVert A_i x + b_i \rVert_2 \leq c_i^T x + d_i,\quad i = 1,\dots,m \]- Parameters:
f
- fconstraints
- the SOCP constraints
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