NLopt Introduction

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NLopt

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NLopt manual

Introduction

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In this chapter of the manual, we begin by giving a general overview of the optimization problems that NLopt solves, the key distinctions between different types of optimization algorithms, and comment on ways to cast various problems in the form NLopt requires. We also describe the background and goals of NLopt.

Optimization problems

NLopt addresses general nonlinear optimization problems of the form:

,

where f is the objective function and x represents the n optimization parameters. This problem may be subject to the bound contraints

for

given lower bounds lb and upper bounds ub (which may be −∞ and/or +∞, respectively, for partially or totally unconstrained problems). One may also optionally have m nonlinear inequality constraints

for .

A point x that satisfies all of the bound and inequality constraints is called a feasible point, and the set of all feasible points is the feasible region.

Global versus local optimization

Gradient-based versus derivative-free algorithms

Equivalent formulations of optimization problems

Background and goals of NLopt