Implementing a smooth exact penalty function for equality-constrained nonlinear optimization

We develop a general equality-constrained nonlinear optimization algorithm based on a smooth penalty function proposed by Fletcher (1970). Although it was historically considered to be computationally prohibitive in practice, we demonstrate that the computational kernels required are no more expensive than other widely accepted methods for nonlinear optimization. The main kernel required to evaluate the penalty function and its derivatives is solving a structured linear system. We show how to solve this system efficiently by storing a single factorization each iteration when the matrices are available explicitly. We further show how to adapt the penalty function to the class of factorization-free algorithms by solving the linear system iteratively. The penalty function therefore has promise when the linear system can be solved efficiently, e.g., for PDE-constrained optimization problems where efficient preconditioners exist. We discuss extensions including handling simple constraints explicitly, regularizing the penalty function, and inexact evaluation of the penalty function and its gradients. We demonstrate the merits of the approach and its various features on some nonlinear programs from a standard test set, and some PDE-constrained optimization problems

Developing international business relationships in a Russian context

The collapse of the former Soviet Union has opened up a wealth of business opportunities for companies seeking new markets in the Russian Federation. Despite this, firms intending to do business in Russia have found themselves hampered by cultural differences in business practices and expectations. As Russia integrates into the global economy, understanding such practices and the managerial mindset of business people is crucial for managers who hope to navigate Russia's complex markets. This study draws on the trust literature and adopts quantitative tools to deconstruct the Russian 'Sviazi' system of social capital business networking. We develop a model isolating three dimensions of Sviazi: one an affective or emotional component; the second, a conative component; and the third, a cognitive component. The model provides a useful guide for helping foreign firms to succeed in Russia, while also serving as a basis for further research in the field. Keywords

Prime generating Lucas sequences

The distribution of prime numbers in Lucas sequences was investigated by independently changing the initial values and the multiplicative constants in the recursive definition of the sequence. The prime distribution was obtained by counting the number of primes in the first 1000 terms of various Lucas sequences. It was found that both smaller seeds and smaller multipliers produced more primes on average than if the seeds and multipliers were large. It was also determined that changing the initial seeds produced more primes and more variation in prime counts than changing the multipliers.Science, Faculty ofUnreviewedUndergraduat

SIGCOMM 1991 A Study of Priority Pricing in Multiple Service Class Networks

We study the role of pricing policies in multiple service class networks. We argue that some form of graduated prices are required in order for a ng multiclass service discipline to have the desired effect. Moreover, we demonstrate through simulation that it is possible to set the prices so that every user is more satisfied with the combined cost and performance of a network with graduated prices. For some users the performance penalty received for requesting a less-than-optimaJ service class is offset by the reduced price of the service. For the other users the monetary penalty incurred by using the more expensive, higher quality service classes is offset by the improved performance they receive. Thus, prices allow us to spread the benefits of multiple service classes around to all users, rather than just having these benefits remain exclusively with users who are performance sensitive.