# A Bundle Algorithm Applied to Bilevel Programming Problems by Dempe S.

By Dempe S.

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Extra info for A Bundle Algorithm Applied to Bilevel Programming Problems with Non-Unique Lower Level Solutions

Sample text

The numerical simulation of discrete-time models is much simpler and quicker, which makes them wel) suited to real-lime process control. Their use, however, may entail some loss of information on the behaviour of the underlying continuous-time system. As in the continuous-time cac;e, one may employ a discrete·time stale-space model = f[xU), p. uCt), tJ, = h[x(t), p, net), 1], x(t+ 1) Ym(t) xeD) =xo(p), where t is now an integer time index, which corresponds to actual lime IT if the underlying continuous-time system is sampled with period T.

This may be remedied by using as the noise n(t) a linear combination of the successive realizations of £(1), called a Moving A \Jerage (or MA). giving y(t) + (/~y(1-I) + ... + a~uYU-n::) = b~ 11(1-11;) + ... + b~bll(t-llb-Il;+ I) * * * + £(t) + c]£(t-l) + ... e. autoregressive part = exogenous part + moving-average parl. Once 12,h lib, lie and llr have been chosen, the unknown parameters arc Such a structure is called AR1I1AX (AutoRegressive-Movillg Average with eXogel/ous variable) or CARMA (Colltrolled AutoRegressive Moving Average).

1993). 2 Discrete .. time models The ever-increasing availability of computers has in many domains dealt a fala] blow to the supremacy of continuous-time models. The numerical simulation of discrete-time models is much simpler and quicker, which makes them wel) suited to real-lime process control. Their use, however, may entail some loss of information on the behaviour of the underlying continuous-time system. As in the continuous-time cac;e, one may employ a discrete·time stale-space model = f[xU), p.