New Feature: Quadratic Constraints (QC)

[Lhongpei]

🚀 Summary of Changes

This pull request introduces support for Quadratic Constraints (QC) in the .QPS/.mps file format, extending the package's capability from Quadratic Programming (QP) to Quadratically Constrained Quadratic Programming (QCQP).

This enhancement allows users to define constraints of the form $L_i \le a_i^\top x + x^\top Q_i x \le U_i$.

✨ Key Features and Updates

• QCQP Support: The core problem representation has been updated to include quadratic constraints.
• New Data Structure: QPSData now includes the qcdata field (Dict{Int, Tuple{Vector{Int}, Vector{Int}, Vector{Float64}}}) to store the constraint-specific quadratic terms ($Q_i$).
• QCMATRIX Section Parsing: Implements logic to correctly identify and parse data within the new QCMATRIX section header in the .QPS/.mps file.
• Documentation Update: The README.md has been revised to reflect the new, more general problem format (including $Q_0$ for the objective and $Q_i$ for constraints).

📖 Updated Problem Format (README.md)

The problem format now officially supported is:

$$\text{optimize} \quad c_0 + c^\top x + \frac{1}{2} x^\top Q_0 x$$ $$\text{subject to} \quad L_i \le a_i^\top x + x^\top Q_i x \le U_i \quad \text{and} \quad \ell \le x \le u$$

🛠️ Implementation Details

• src/readqps.jl:
  • Added const QCMATRIX = 11 to section headers.
  • Updated read_card! to recognize and handle the QCMATRIX section, which requires a row name (card.f2).
  • Implemented read_qcmatrix_line! to process the variable indices and values for the quadratic constraint matrix $Q_i$ based on the current constraint index (current_qc_row_idx).
  • Modified readqps to track current_qc_row_idx and handle the initialization and processing of the QCMATRIX section.

This change significantly broadens the class of optimization problems that can be read by QPSReader.jl.