At present, many metropolitan sewer systems do not meet existing and proposed standards on water pollution. Existing systems were designed to overflow at prescribed locations in order to protect the sewage treatment plants whenever severe overload conditions exist (usually during storms). This discharge of untreated overflows into natural receiving waters is of growing concern to water pollutio...

We investigate the simultaneous regularization and discretization of an optimal control problem with pointwise control constraints. Typically such problems exhibit bang-bang solutions: the optimal control almost everywhere takes values at the control bounds. We derive discretization error estimates that are robust with respect to the regularization parameter. These estimates can be used to make...

The past decade has seen a variety of operating modifications for Simulated Moving Bed (SMB) processes, including Three-Zone, VARICOL, and PowerFeed. In recent studies, we have shown that these can all be embedded within a superstructure optimization problem with timevariant flow rates. Moreover, the resulting dynamic optimization problem has yielded a number of interesting and useful insights ...

The paper presents a scheme for obtaining a linear-feedback law for a linear system as a result of minimizing a quadratic-performance index; the resulting closed-loop system has the property that all its poles lie in a halfplane Re (s) < -a, where a >0 may be chosen by the designer. The advantages of this arrangement over conventional optimal design are considered. In particular, it is shown th...

A variable annuity contract with Guaranteed Minimum Withdrawal Benefit (GMWB) promises to return the entire initial investment through cash withdrawals during the policy life plus the remaining account balance at maturity, regardless of the portfolio performance. We assume that market is complete in financial risk and also there is no mortality risk (in the event of policyholder death, the cont...

The Switch Point Algorithm is a new approach for solving optimal control problems whose solutions are either singular or bang-bang both and bang-bang, which possess finite number of jump discontinuities in an at the points time where solution structure changes. Problems this class can often be reduced to optimization over switching points. Formulas derived derivative objective with respect swit...

with zi ∈ { Ĉ[0, T ] |zi(0) = 0, zi(T ) = bi } , with technical constraints for the consumption rate over time: mi ≤ żi(t) ≤Mi, ∀i = 1, . . . , n. We abstract from this situation to tackle a general problem which studies a production process whose efficiency of production with respect to each input depends on time, on the stock of the various inputs, and on the consumption rate of other inputs....