Class SOCPGeneralProblem

  • 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:
    • Constructor Detail

      • 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 - f
        constraints - the SOCP constraints
      • 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 - f
        constraints - the SOCP constraints