- Tytuł:
- Fixed-point iteration based algorithm for a class of nonlinear programming problems
- Autorzy:
- Belegundu, A. D.
- Powiązania:
- https://bibliotekanauki.pl/articles/122443.pdf
- Data publikacji:
- 2017
- Wydawca:
- Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
- Tematy:
-
fixed-point iteration
resource allocation
nonlinear programming
optimality criteria
iteracja punku stałego
alokacja zasobów
programowanie nieliniowe
kryteria optymalizacji dwukierunkowych torów wodnych
algorytm punktu stałego - Opis:
- A fixed-point algorithm is presented for a class of singly constrained nonlinear programming (NLP) problems with bounds. Setting the gradient of the Lagrangian equal to zero yields a set of optimality conditions. However, a direct solution on general problems may yield non-KKT points. Under the assumption that the gradient of the objective function is negative while the gradient of the constraint function is positive, and that the variables are positive, it is shown that the fixed-point iterations can converge to a KKT point. An active set strategy is used to handle lower and upper bounds. While fixed-point iteration algorithms can be found in the structural optimization literature, these are presented without clearly stating assumptions under which convergence may be achieved. They are also problem specific as opposed to working with general functions f, g. Here, the algorithm targets general functions which satisfy the stated assumptions. Further, within this general context, the fixed-point variable update formula is given physical significance. Unlike NLP descent methods, no line search is involved to determine step size which involves many function calls or simulations. Thus, the resulting algorithm is vastly superior for the subclass of problems considered. Moreover, the number of function evaluations remains independent of the number of variables allowing the efficient solution of problems with a large number of variables. Applications and numerical examples are presented.
- Źródło:
-
Journal of Applied Mathematics and Computational Mechanics; 2017, 16, 2; 29-41
2299-9965 - Pojawia się w:
- Journal of Applied Mathematics and Computational Mechanics
- Dostawca treści:
- Biblioteka Nauki
Artykuł