Office of Academic Resources
Chulalongkorn University
Chulalongkorn University

Home / Help

AuthorRubinov, Alexander. author
TitleLagrange-type Functions in Constrained Non-Convex Optimization [electronic resource] / by Alexander Rubinov, Xiaoqi Yang
ImprintBoston, MA : Springer US : Imprint: Springer, 2003
Connect tohttp://dx.doi.org/10.1007/978-1-4419-9172-0
Descript XIV, 286 p. online resource

SUMMARY

Lagrange and penalty function methods provide a powerful approach, both as a theoretical tool and a computational vehicle, for the study of constrained optimization problems. However, for a nonconvex constrained optimization problem, the classical Lagrange primal-dual method may fail to find a miniยญ mum as a zero duality gap is not always guaranteed. A large penalty parameter is, in general, required for classical quadratic penalty functions in order that minima of penalty problems are a good approximation to those of the original constrained optimization problems. It is well-known that penaity functions with too large parameters cause an obstacle for numerical implementation. Thus the question arises how to generalize classical Lagrange and penalty functions, in order to obtain an appropriate scheme for reducing constrained optimizaยญ tion problems to unconstrained ones that will be suitable for sufficiently broad classes of optimization problems from both the theoretical and computational viewpoints. Some approaches for such a scheme are studied in this book. One of them is as follows: an unconstrained problem is constructed, where the objective function is a convolution of the objective and constraint functions of the original problem. While a linear convolution leads to a classical Lagrange function, different kinds of nonlinear convolutions lead to interesting generalizations. We shall call functions that appear as a convolution of the objective function and the constraint functions, Lagrange-type functions


Mathematics Convex geometry Discrete geometry Mathematical optimization Operations research Management science Mathematics Optimization Operations Research Management Science Convex and Discrete Geometry



Location



Office of Academic Resources, Chulalongkorn University, Phayathai Rd. Pathumwan Bangkok 10330 Thailand

Contact Us

Tel. 0-2218-2929,
0-2218-2927 (Library Service)
0-2218-2903 (Administrative Division)
Fax. 0-2215-3617, 0-2218-2907

Social Network

  line

facebook   instragram