This note reports a correction to the results obtained by [2], in which an error was unfortunately discovered during work with D. Robinson. The problem is in the proof of Lemma 3.10 of this reference, where it is claimed that Lemma 6.5.3 of [1] can be invoked to deduce that ρc k ≥ η2, where ρc k is a specific ratio of achieved to predicted reduction is constraint violation and η2 is a constant ...

This chapter considers the multiple change–point problem for time series, including strongly dependent processes, with an unknown number of change– points. We propose an adaptive method for finding the segmentation, i.e., the sequence of change–points τ with the optimal level of resolution. This optimal segmentation τ̂ is obtained by minimizing a penalized contrast function J(τ , y)+βpen(τ ). Fo...

For the existing problem of user reliability computing in open knowledge organization, the current related researches are analyzed, and then this paper puts forward a dynamic computational method of user reliability based on multi-attribute evaluation. The method introduces direct reliability, bonus-penalty factor, group consumption factor and user consumption factor to compute the user reliabi...

We extend the theory of penalty functions to stochastic programming problems with nonlinear inequality constraints dependent on a random vector with known distribution. We show that the problems with penalty objective, penalty constraints and chance constraints are asymptotically equivalent under discretely distributed random parts. This is a complementary result to Branda (2012a), Branda and D...

We study a discrete-time interaction risk model with delayed claims within the framework of the compound binomial model. Using the technique of generating functions, we derive both a recursive formula and a defective renewal equation for the expected discounted penalty function. As applications, the probabilities of ruin and the joint distributions of the surplus one period to ruin and the defi...

We present a chaotic hybrid invasive weed optimization (CHIWO) algorithm with an adaptive penalty function which is introduced to solve the constraints for solving the machinery optimizing problems. The proposed CHIWO algorithm runs consistently well on the studies of 13 Benchmark functions and 3 machinery optimizing problems. Experimental results indicate that CHIWO algorithm is a simple and e...

This paper introduces a global approach to the semi-infinite programming problem that is based upon a generalisation of the g~ exact penalty function. The advantages are that the ensuing penalty function is exact and the penalties include all violations. The merit function requires integrals for the penalties, which provides a consistent model for the algorithm. The discretization is a result o...