Scholarly record

COMPARISON OF CONSTRAINED OPTIMIZATION FUNCTIONS

Bogdan Constantin, Nan Marin Silviu, Grecea Danut, Mamara Nicoleta Loredana

Abstract

Numerical algorithms for constrained nonlinear optimization can be broadly categorized into gradient-based methods and direct search methods. Gradient search methods use first derivatives (gradients) or second derivatives (Hessians) information. Examples are the sequential quadratic programming (SQP) method, the augmented Lagrangian method, and the (nonlinear) interior point method. Direct search methods do not use derivative information. Examples are Nelder|Mead, genetic algorithm and differential evolution, and simulated annealing. Direct search methods tend to converge more slowly, but can be more tolerant to the presence of noise in the function and constraints. Typically, algorithms only build up a local model of the problems. Furthermore, to ensure conver - gence of the iterative process, many such algorithms insist on a certain decrease of the objective function or of a merit function which is a combination of the objective and constraints. Such algorithms will, if convergent, only find the local optimum, and are called local optimization algorithms. In Mathematica local optimization problems can be solved using FindMinimum. Global optimization algorithms, on the other hand, attempt to find the global optimum, typically by allowing decrease as well as increase of the objective/merit function. Such algorithms are usually computationally more expensive. Global optimization problems can be solved exactly using Minimize or numerically using NMinimize. NMinimize, NMaximize, Minimize and Maximize employ global optimization algorithms, and are thus suitable when a global optimum is needed. Minimize and Maximize can find exact global optima for a class of optimization problems containing arbitrary polynomial problems. However, the algorithms used have a very high asymptotic complexity and therefore are suitable only for problems with a small number of variables.

Publication Impact Profile

• Citations
• Scopus - Citation Indexes: 1

• Captures
• Mendeley - Readers: 1

PLUMX see details

DOI resolver: doi.org/10.5593/sgem2017/21/s07.028

Publication details

Back to publication list