PDHCG-CQP: A First-Order Solver for Conic QPs

[Lhongpei]

This PR will extend PDHCG to Conic QPs with following formulation:

$$\begin{aligned} \min_{x} \quad & \frac{1}{2}x^\top (Q + R^\top D R) x + c^\top x \\\ \text{s.t.} \quad & \ell_c \le Ax \le u_c, \\\ & Fx + g \in \mathcal{K}_a, \\\ & \ell_v \le x \le u_v, \\\ & x_J \in \mathcal{K}_v \quad \text{for variable-cone blocks } J. \end{aligned}$$

• $Q$ is the sparse symmetric quadratic component (optional).
• $R \in \mathbb{R}^{k\times n}$ is a tall low-rank factor (optional, $k$ = rank).
• $D \in \mathbb{R}^{k\times k}$ is an optional middle matrix that scales / weights / signs the low-rank term. When omitted it defaults to the identity, recovering the standard $Q + R^\top R$ formulation. $D$ may be diagonal, sparse, dense, or indefinite — the backend auto-detects the cheapest runtime representation.
• Standard SOC, Rotated SOC, Exponential, and Power cones are supported both on variable blocks and through native affine constraints $Fx + g \in \mathcal{K}_a$.