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.