SAGE — Solver-Augmented Grounding Engine

Connects Claude to production optimization solvers (HiGHS, OSQP, OR-Tools) via local MCP. Exposes tools to solve LP, MIP, quadratic portfolio problems, and workforce scheduling from JSON or Excel. The check_feasibility tool computes irreducible infeasible sets and ranks constraint relaxations when no solution exists, which is often more valuable than approximate answers. Returns dual values, reduced costs, and shadow prices for sensitivity analysis. Also includes read_data_file for ingesting spreadsheets and generate_template for scaffolding problem structure. Runs synchronously but supports iterative solvers that can checkpoint and resume. Useful when you need mathematically certified solutions instead of LLM approximations for resource allocation, scheduling, or portfolio construction.