Adjustable robust optimization through multi-parametric programming

Adjustable robust optimization (ARO) involves recourse decisions (i.e. reactive actions after the realization of the uncertainty, ‘wait-and-see’     

A multi-parametric programming approach for multilevel hierarchical and decentralised optimisation problems

In this paper, we outline the foundations of a general global optimisation strategy for the solution of multilevel hierarchical and general decentralised multilevel problems, based on our recent developments on multi-parametric programming and control theory. The core idea is to recast each optimisation subproblem, present in the hierarchy, as a multi-parametric programming problem, with parameters being the optimisation variables belonging to the remaining subproblems. This then transforms the multilevel problem into single-level linear/convex optimisation problems. For decentralised systems, where more than one optimisation problem is present at each level of the hierarchy, Nash equilibrium is considered. A three person dynamic optimisation problem is presented to illustrate the mathematical developments.     

Methane activation on a La0.6Sr0.4Co0.8Fe0.2O3 perovsksite; catalytic and electrocatalytic results

The catalytic and electrocatalytic behaviour of the La_0.6Sr_0.4Co_0.8Fe_0.2O₃ (LSCF) perovskite deposited on yttria stabilized zirconia (YSZ), was studied during the reaction of methane oxidation. Experiments were carried out at atmospheric pressure, and at temperatures between 600 and 900 °C. When, instead of cofeeding with methane in the gas phase, oxygen was electrochemically supplied as O²⁻, considerable changes in the methane conversion and product selectivity were observed. The non-faradaic effects (NEMCA) were also studied and compared to those observed with metal catalysts. Paper presented at the 4th Euroconference on Solid State Ionics, Renvyle, Galway, Ireland, Sept. 13–19, 1997     

Bonding and ion-ion interactions of Mn ions in fluoride-phosphate and boro-silicate glasses probed by EPR and fluorescence spectroscopy

Electron paramagnetic resonance (EPR) and fluorescence spectroscopy are sensitive and selective methods for probing coordination and bonding of Mn²⁺ ions in glasses. Both methods provide additional information on Mn-Mn ion interactions and cluster formation. Mn²⁺ was found to be tetrahedrally coordinated in boro-silicate glasses of high optical basicity, and octahedrally coordinated in low alkaline boro-silicate glasses (duran-type) as in fluoride-phosphate glasses. Broad emission bands and multicomponent fluorescence decay curves in duran glasses indicate very strong Mn-Mn ion interactions and the presence of multiple Mn²⁺ sites. Site distribution is more homogenous in metaphosphate glasses, though concentration quenching is apparent at high Mn-levels. As the Mn-content increases the EPR spectra show exchange narrowing due to a decrease in the Mn-Mn distances in the duran series, but show extreme linewidth broadening due to increased cluster sizes at constant Mn-Mn distances for metaphosphate glasses. For the fluoride-phosphate and boro-silicate systems investigated, fluorescence lifetimes are found to decrease as the wavelength of the emission maximum increases and with increasing g-values of the sextet at g = 2. For octahedral coordination of Mn²⁺ ions the EPR hyperfine splitting constant decreases linearly with increasing optical basicity, as a result of an increasing covalent character of the Mn²⁺-ligand bond.     

Catalytic behavior of La0.6Sr0.4Co0.8Fe0.2O3 perovskite-type oxide thin films deposited on YSZ during the reaction of ethanol oxidation

The perovskite-type oxide La_0.6Sr_0.4Co_0.8Fe_0.2O₃ was studied as an ethanol oxidation catalyst-anode as a probable candidate for future application in Solid Oxide Fuel Cells (SOFCs). The investigation was carried out at atmospheric total pressure in a fully Yttria-Stabilized Zirconia (YSZ) continuous stirred tank reactor (C.S.T.R.) at a temperature range between 300–700 °C. Preliminary results show that La_0.6Sr_0.4Co_0.8Fe_0.2O₃ thin films deposited on the inner bottom of the one end closed YSZ tube present: a) mediocre ethanol oxidation catalytic activity at relatively low temperature values and b) thermal stability under the experimental conditions. Paper presented at the 5th Euroconference on Solid State Ionics, Benalmádena, Spain, Sept. 13–20, 1998.     

Development and validation of a rapid HPLC method for the determination of five banned fat-soluble colorants in spices using a narrow-bore monolithic column

This work reports a fast and simple liquid chromatographic method for the simultaneous determination of five banned fat-soluble synthetic colorants, namely Sudan I-IV and Para-Red, in spice samples. The analytes were successfully separated isocratically in less than 5 min on the new narrow bore monolithic column, FastGradient^® Chromolith (50 mm × 2.0 mm i.d.) using a mobile phase of 0.1% (v/v) HCOOH/acetonitrile (35/65%, v/v) at a flow rate of 1.5 mL min⁻¹. All colorants were detected at 506 nm. The main parameters (mobile phase composition, flow rate, injection volume) affecting the separation were studied. The proposed method was thoroughly validated in terms of linearity, LODs, precision and accuracy. The method was applied to the determination of the studied azo-dyes in various spices (paprika, chilli and mixed spice powders) after ultrasound-assisted extraction. Satisfactory recoveries, ranging from 92% to 109% were obtained.     

A “Discretization” Technique for the Solution of ODEs II

A functional analytic technique was recently presented for finding discrete equivalent counterparts of initial value problems of ODEs and obtaining their real analytic solutions. In the current paper, this technique is extended to boundary value problems of ODEs and to the complex solutions of ODEs. In order to demonstrate this technique, it is applied to the classic Blasius problem of fluid mechanics. Apart from its real solution, its complex solution is also studied. The obtained results indicate that the complex Blasius function exhibits an oscillatory behavior and strengthen a conjecture regarding its singularities in the complex plane.     

Thermogravimetric study of the surfactant–diethanolamine–titanium isopropoxide system behavior

Mesoporous anatase TiO₂ materials with specific surface areas between 70 and 110 m² g^?1 were prepared via sol–gel technique using surfactants oleic acid and Triton-X (TX), in the presence or absence of diethanolamine, in methanol. Surfactants like TX or oleic acid (OA), as well as a gelating and chelate agent like diethanolamine (DEA) are commonly used in TiO₂ formation from a titanium isopropoxide solution. Thermogravimetric methods were applied in order to evaluate the effect of the addition of such molecules in a precursor suspension before TiO₂ materials preparation. The in situ investigation of such systems showed that numerous interactions occur between large molecules such as TX and OA that attributed on both steric effects and hydrogen bond formation. Materials prepared through modified sol–gel technique seem to be stabilized through DEA addition in the precursor suspension.     

Theoretical and algorithmic advances in multi-parametric programming and control

This paper presents an overview of recent theoretical and algorithmic advances, and applications in the areas of multi-parametric programming and explicit/multi-parametric model predictive control (mp-MPC). In multi-parametric programming, advances include areas such as nonlinear multi-parametric programming (mp-NLP), bi-level programming, dynamic programming and global optimization for multi-parametric mixed-integer linear programming problems (mp-MILPs). In multi-parametric/explicit MPC (mp-MPC), advances include areas such as robust multi-parametric control, multi-parametric nonlinear MPC (mp-NMPC) and model reduction in mp-MPC. A comprehensive framework for multi-parametric programming and control is also presented. Recent applications include a hydrogen storage device, a fuel cell power generation system, an unmanned autonomous vehicle (UAV) and a hybrid pressure swing adsorption (PSA) system.     

A global optimization algorithm for generalized semi-infinite,continuous minimax with coupled constraints and bi-level problems

We propose an algorithm for the global optimization of three problem classes: generalized semi-infinite, continuous coupled minimax and bi-level problems. We make no convexity assumptions. For each problem class, we construct an oracle that decides whether a given objective value is achievable or not. If a given value is achievable, the oracle returns a point with a value better than or equal to the target. A binary search is then performed until the global optimum is obtained with the desired accuracy. This is achieved by solving a series of appropriate finite minimax and min-max-min problems to global optimality. We use Laplace’s smoothing technique and a simulated annealing approach for the solution of these problems. We present computational examples for all three problem classes.