Optimizer Problems

A central object in SimpleSolvers are optimizer problems (see SimpleSolvers.AbstractOptimizerProblem). They are either SimpleSolvers.LinesearchProblems or OptimizerProblems. The goal of a solver (both LinearSolvers and NonlinearSolvers) is to make the optimizer problem have value zero. The goal of an Optimizer is to minimize a OptimizerProblem.

Examples

Multivariate Optimizer Problems

OptimizerProblems are used in a way similar to LinesearchProblems, the difference is that the derivative functions are replaced by gradient functions, i.e.:

• derivative $\implies$ gradient,
• derivative! $\implies$ gradient!,
• derivative!! $\implies$ gradient!!.

f(x::AbstractArray) = sum(x .^ 2)
x = rand(3)

obj = OptimizerProblem(f, x)

OptimizerProblem (for vector-valued quantities only the first component is printed):

    f(x)              = NaN 
    g(x)₁             = NaN 
    x_f₁              = NaN 
    x_g₁              = NaN 

Every instance of OptimizerProblem stores an instance of Gradient to which we similarly can apply the functions gradient or gradient!:

grad = GradientAutodiff(f, x)
gradient!(obj, grad, x)

3-element Vector{Float64}:
 1.042427591070766
 1.1736135149066969
 1.7817573961855622

The difference to Gradient is that we also store the value for the evaluated gradient, which can be accessed by calling:

gradient(obj)

3-element Vector{Float64}:
 1.042427591070766
 1.1736135149066969
 1.7817573961855622