Research on the Dual Problem of Trust Region Bundle Method
Journal Title: Journal of Advances in Mathematics and Computer Science - Year 2017, Vol 22, Issue 3
Abstract
With the rapid development of science and technology as well as the cross-integration between the various disciplines, the nonsmooth optimization problem plays an increasingly important role in operational research. In this paper, we use the trust region method to study nonsmooth unconstrained optimization problems. Trust region subproblem is constructed to produce the next iteration point by using feasible set as constraint condition. As the number of iterations increases, the compression principle is used to control the elements in a bundle of information. And then the subproblem is studied by Lagrangian function and penalized bundle method [1]. The optimal solution and the relevant derivative conclusion are obtained by transforming the primal problem and dual problem into each other.
Authors and Affiliations
Jie Shen, Ya-Li Gao
Existence and Stability of Equilibrium Points under Combined Effects of Oblateness and Triaxiality in the Restricted Problem of Four Bodies
The restricted four-body problem consists of an infinitesimal body which is moving under the Newtonian gravitational attraction of three finite bodies The three bodies (primaries) lie always at the vertices of an equila...
Computation of k-out-of-n System Reliability via Reduced Ordered Binary Decision Diagrams
A prominent reliability model is that of the partially-redundant (k-out-of-n) system. We use algebraic as well as signal-flow-graph methods to explore and expose the AR algorithm for computing k-out-of-n reliability. We...
Hellinger Distance Between Generalized Normal Distributions
A relative measure of informational distance between two distributions is introduced in this paper. For this purpose the Hellinger distance is used as it obeys to the definition of a distance metric and, thus, provides a...
A Stochastic Model of the Dynamics of Stock Price for Forecasting
In this work, a stochastic model of some selected stocks in the Nigerian Stock Exchange (NSE) is formulated. We considered four different stocks and their market prices. The likelihood of each change occurring in the sto...
The Behrens-Fisher Problem: A Z Distribution Approach
We propose the Z distribution to tackle the Behrens-Fisher problem. First, we define the Z distribution which is a generalization of the t distribution, and then find the pdf and cdf of the Z distribution. After that, we...