Hatim Djelassi

A hybrid discretization algorithm with guaranteed feasibility for the global solution of semi-infinite programs

A discretization-based algorithm for the global solution of semi-infinite programs (SIPs) is proposed, which is guaranteed to converge to a feasible,

Comparing Optimization Algorithms for Shape Optimization of Extrusion Dies

\varepsilon

Bounded-error optimal experimental design via global solution of constrained min-max program

ε-optimal solution finitely under mild assumptions. The algorithm is based on the hybridization of two existing algorithms. The first algorithm (Mitsos in Optimization 60(10–11):1291–1308, 2011) is based on a restriction of the right-hand side of the constraints of a discretized SIP. The second algorithm (Tsoukalas and Rustem in Optim Lett 5(4):705–716, 2011) employs a discretized oracle problem and a binary search in the objective space. Hybridization of the approaches yields an algorithm, which leverages the strong convergence guarantees and the relatively tight upper bounding problem of the first approach while employing an oracle problem adapted from the second approach to generate cheap lower bounds and adaptive updates to the restriction of the first approach. These adaptive updates help in avoiding a dense population of the discretization. The hybrid algorithm is shown to be superior to its predecessors both theoretically and computationally. A proof of finite convergence is provided under weaker assumptions than the assumptions in the references. Numerical results from established SIP test cases are presented.

Parameter estimation for cubic equations of state models subject to sufficient criteria for thermodynamic stability

Abstract The optimal solution in dynamic optimization of batch processes often exhibits active path constraints. The goal of this work is the robust satisfaction of path constraints in the presence of parametric uncertainties based on known worst-case formulations. These formulations are interpreted as semi-infinite programs (SIP). Two known SIP algorithms are extended to the dynamic case and assessed. One is a discretization approach and the other a local reduction approach. With these presented concepts, robust path constraint satisfaction is in principle guaranteed. In this work, however, local methods are used to approximate the global solution of the lower-level problem with local solvers thus allowing for (rather unlikely) constraint violations. Finally, the penicillin fermentation is introduced as a well-known case study with uncertainties, which is modified in this work by adding further dependencies. The adaptation of the SIP concepts to dynamic optimization problems are shown to be successful for this case study.