biogeme-optimization 0.0.10

Description:

biogemeoptimization 0.0.10

biogeme-optimization

Various optimization algorithms used for teaching and research. In particular, they are used by Biogeme.
The package contains the following modules:
algebra
It contains functions dealing with linear algebra:

A modified Cholesky factorization introduced by Schnabel and Eskow (1999)
The calculation of a descent direction based on this factorization.

bfgs
The functions in this module calculate

the BFGS update of the hessian approximation (see Eq. (13.12) in Bierlaire (2015)),
the inverse BFGS update of the hessian approximation (see Eq. (13.13) in Bierlaire (2015)).

bounds
This module mainly defines the class Boundsthat manages the bound constraints.
diagnostics
This module defines the diagnostic of some optimization subproblems
(dogleg, and comjugate gradient).
exceptions
It defines the OptimizationError exception.
format
It defines the class FormattedColumns that formats the information
reported at each iteration of an algorithm.
function
It defines the abstract class FunctionToMinimize that encapsulate
the calculation of the objective function and its derivatives.
hybrid_function
It defines the class HybridFunction that calculates the objective
function and its derivatives, where the second derivative can be
either the analytical hessian, or a BFGS approximation.
linesearch
This module implements the line search algorithms (see Chapter 11 in Bierlaire, 2015).
simple_bounds
This module implements the minimization algorithm under bound
constraints proposed by Conn et al. (1988).
trust_region
This module implements the trust region algorithms (see Chapter 12 in
Bierlaire, 2015).
References

Bierlaire, M. (2015). Optimization: Principles and
Algortihms. EPFL
Press.
Conn, A. R., Gould, N. I. M and Toint, Ph. L. (1988) Testing a
Class of Methods for Solving Minimization Problems with Simple
Bounds on the
Variables. Mathematics
of Computation, 50(182), 399-430.
Schnabel, R. B. and Eskow, E. (1999) A Revised Modified Cholesky Factorization Algorithm. SIAM Journal on Optimization, 9(4), 1135-1148.