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Simplex Optimizer is an interactive platform for solving mathematical optimization problems. It ships a Python/FastAPI backend that exposes a clean REST API and a React 18 frontend that visualizes results — including simplex tableaux, feasible-region plots, Branch & Bound trees, and 3D surface graphs — all in the browser.

Quickstart

Run the backend and frontend locally in under five minutes.

Optimization Methods

Explore all nine supported solvers — from Simplex to KKT conditions.

API Reference

Full REST endpoint documentation with request/response schemas.

Architecture

Understand how the FastAPI backend and React frontend fit together.

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Supported Methods

Simplex Optimizer covers the full spectrum of classical optimization techniques:

Simplex (Big-M)

Linear programming with 2–5 variables. Outputs the full iteration tableau.

Graphical LP

2-variable LP with feasible-region visualization and optimal-point overlay.

Binary Integer

0/1 integer programming via Branch & Bound with full exploration tree.

Pure Integer

General integer programming via Branch & Bound with variable bounding.

Bisection

Single-variable unconstrained optimization via bisection on f′(x).

Newton-Raphson

Fast single-variable optimization using second-order Newton updates.

Gradient Descent

Multivariable unconstrained optimization via gradient ascent/descent.

Graphical Multivar

Surface and volume plots for 2–3 variable functions with critical points.

KKT Conditions

Constrained nonlinear programming via Karush-Kuhn-Tucker conditions.

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Get Running in Minutes

1

Start the backend

cd backend
python -m venv .venv && source .venv/bin/activate
pip install -r requirements.txt
uvicorn app.main:app --reload --port 8000
2

Start the frontend

cd frontend
npm install
npm run dev
3

Open the app

Visit http://localhost:5173 in your browser, or explore the auto-generated API docs at http://localhost:8000/docs.
4

Make your first API call

curl -X POST http://localhost:8000/api/v1/simplex/solve \
  -H "Content-Type: application/json" \
  -d '{"objective":[3,2],"goal":"max","constraints":[{"coefficients":[1,1],"inequality":"<=","rhs":4},{"coefficients":[1,0],"inequality":"<=","rhs":3}]}'
The API is fully documented via Swagger UI at http://localhost:8000/docs and ReDoc at http://localhost:8000/redoc when the backend is running.

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