> ## Documentation Index
> Fetch the complete documentation index at: https://docs.fincept.in/llms.txt
> Use this file to discover all available pages before exploring further.

# Minimize Multi-Variable Function

> Find the minimum of a multi-variable function f(x) where x is a vector. Supports built-in test functions: rosenbrock (banana-shaped valley, tests optimization robustness), sphere (simple convex function), rastrigin (many local minima), quadratic (ellipsoidal contours). Methods: bfgs (Quasi-Newton method, uses gradient approximations, fast and reliable), nelder_mead (simplex method, derivative-free, robust for non-smooth functions). Essential for portfolio optimization, parameter calibration, maximum likelihood estimation, and model fitting. [Tier: BASIC, Credits: 1]



## OpenAPI

````yaml api-specs/numerical.json post /quantlib/numerical/optimize/minimize
openapi: 3.1.0
info:
  title: FinceptQuantLib API - Numerical
  description: >-
    Numerical module endpoints for FinceptQuantLib API. The Numerical module
    (Basic Tier, 1 credit per request) provides comprehensive numerical methods
    including finite difference differentiation, Fast Fourier Transform (FFT),
    numerical integration (quadrature and Monte Carlo), interpolation methods
    (linear, cubic, spline), linear algebra operations (matrix decomposition,
    solving systems), ODE solvers, root finding algorithms, optimization
    methods, and nonlinear least squares fitting. Essential for quantitative
    analysis, scientific computing, and numerical model implementation.
  version: 3.0.0
  contact:
    name: Fincept API Support
    url: https://fincept.in
servers:
  - url: https://api.fincept.in
    description: Fincept API Production Server
security:
  - APIKeyHeader: []
tags:
  - name: quantlib-numerical
    description: >-
      Numerical methods including differentiation, FFT, integration,
      interpolation, linear algebra, ODE solvers, root finding, and optimization
    x-displayName: Numerical
paths:
  /quantlib/numerical/optimize/minimize:
    post:
      tags:
        - quantlib-numerical
      summary: Minimize Multi-Variable Function
      description: >-
        Find the minimum of a multi-variable function f(x) where x is a vector.
        Supports built-in test functions: rosenbrock (banana-shaped valley,
        tests optimization robustness), sphere (simple convex function),
        rastrigin (many local minima), quadratic (ellipsoidal contours).
        Methods: bfgs (Quasi-Newton method, uses gradient approximations, fast
        and reliable), nelder_mead (simplex method, derivative-free, robust for
        non-smooth functions). Essential for portfolio optimization, parameter
        calibration, maximum likelihood estimation, and model fitting. [Tier:
        BASIC, Credits: 1]
      operationId: minimize
      requestBody:
        required: true
        content:
          application/json:
            schema:
              type: object
              required:
                - func_name
                - x0
              properties:
                func_name:
                  type: string
                  description: Function to minimize
                  enum:
                    - rosenbrock
                    - sphere
                    - rastrigin
                    - quadratic
                  example: rosenbrock
                x0:
                  type: array
                  items:
                    type: number
                  description: Initial guess for the minimum location
                  example:
                    - -1
                    - 2
                method:
                  type: string
                  description: Optimization method
                  enum:
                    - bfgs
                    - nelder_mead
                  default: bfgs
                  example: bfgs
                tol:
                  type: number
                  description: Convergence tolerance
                  default: 1.e-8
                  example: 1.e-8
            example:
              func_name: rosenbrock
              x0:
                - -1
                - 2
              method: bfgs
              tol: 1.e-8
      responses:
        '200':
          description: Successful Response
          content:
            application/json:
              schema:
                type: object
                properties:
                  success:
                    type: boolean
                    example: true
                  data:
                    type: object
                    properties:
                      x:
                        type: array
                        items:
                          type: number
                        description: Location of minimum (Rosenbrock minimum at [1, 1])
                        example:
                          - 1
                          - 1
                      fun:
                        type: number
                        description: Function value at minimum
                        example: 0
                      iterations:
                        type: integer
                        description: Number of iterations required
                        example: 42
                      converged:
                        type: boolean
                        description: Whether the method converged
                        example: true
                      method:
                        type: string
                        description: Method used
                        example: bfgs
              example:
                success: true
                data:
                  x:
                    - 1
                    - 1
                  fun: 0
                  iterations: 42
                  converged: true
                  method: bfgs
        '401':
          $ref: '#/components/responses/UnauthorizedError'
        '402':
          $ref: '#/components/responses/InsufficientTierError'
        '422':
          description: Validation Error
      security:
        - APIKeyHeader: []
components:
  responses:
    UnauthorizedError:
      description: Authentication information is missing or invalid
      content:
        application/json:
          schema:
            type: object
            properties:
              detail:
                type: string
                example: Invalid API key
    InsufficientTierError:
      description: API tier insufficient for this endpoint
      content:
        application/json:
          schema:
            type: object
            properties:
              detail:
                type: string
                example: Endpoint requires Basic tier or higher
  securitySchemes:
    APIKeyHeader:
      type: apiKey
      in: header
      name: X-API-Key
      description: >-
        API key for authentication. Get your key at
        https://api.fincept.in/auth/register

````