Class 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:
    • 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