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# Welcome to the Ipopt home page

## Introduction

Ipopt (**I**nterior **P**oint **OPT**imizer, pronounced I-P-Opt) is a software package for large-scale nonlinear optimization. It is designed to find (local) solutions of mathematical optimization problems of the from

min f(x) x in R^n s.t. g_L <= g(x) <= g_U x_L <= x <= x_U

where
` f(x): R^n --> R `
is the objective function, and
` g(x): R^n --> R^m `
are the constraint functions. The vectors ` g_L ` and ` g_U ` denote the lower and upper bounds on the constraints, and the vectors `x_L` and `x_U` are the bounds on the variables `x`.