Theoretical and practical convergence of a self-adaptive penalty algorithm for constrained global optimization

This paper proposes a self-adaptive penalty function and presents a penalty-based algorithm for solving nonsmooth and nonconvex constrained optimization problems. We prove that the general constrained optimization problem is equivalent to a bound constrained problem in the sense that they have the same global solutions. The global minimizer of the penalty function subject to a set of bound constraints may be obtained by a population-based meta-heuristic. Further, a hybrid self-adaptive penalty firefly algorithm, with a local intensification search, is designed, and its convergence analysis is established. The numerical experiments and a comparison with other penalty-based approaches show the effectiveness of the new self-adaptive penalty algorithm in solving constrained global optimization problems.The authors would like to thank the referees, the Associate Editor and the Editor-in-Chief for their valuable comments and suggestions to improve the paper. This work has been supported by COMPETE: POCI-01-0145-FEDER-007043 and FCT - Funda¸c˜ao para a Ciˆencia e Tecnologia within the projects UID/CEC/00319/2013 and UID/MAT/00013/2013.info:eu-repo/semantics/publishedVersio

Glass fibres from blast furnace slag composition

Continuous fibers (10-13 micrometers diam.) were drawn using ceramic bushings from glasses having compositions similar to that of blast furnace slag. Compositions with 0.5 mol % TiO2 give the strongest fibers. Crystallites 100-2000 Angstroms in size seem to be dispersed uniformly in the glass matrix

Unimolecular reaction dynamics of CH<SUB>3</SUB>COCl and FCH<SUB>2</SUB>COCl : An infrared chemiluminescence and ab initio study

The F+CH<SUB>3</SUB>COCl and H+ICH<SUB>2</SUB>COCl reaction systems were studied by the infrared chemiluminescence method in a flow reactor. The primary reaction of F+CH<SUB>3</SUB>COCl gives a nascent HF(v) distribution of P<SUB>1</SUB>-P<SUB>3</SUB> =21:52:27. A linear surprisal analysis gives P<SUB>0</SUB>=3 and &#402;<SUB>v</SUB>(HF) = 0.60, which is typical for H abstraction reactions by F atoms. The C-H bond energy in acetyl chloride is estimated as &#8804;101.2 kcal mol<SUP>&#8722;1</SUP>, from the highest HF(v, J) level populated in the primary reaction. The H + ICH<SUB>2</SUB>COCl primary reaction leads to HI + CH<SUB>2</SUB>COCl. The secondary F+CH<SUB>2</SUB>COCl and H + CH<SUB>2</SUB>COCl reactions give chemically activated FCH<SUB>2</SUB>COCl/CH<SUB>3</SUB>COCl molecules. The 1,2-HCl elimination channel is the dominant unimolecular pathway for both reactions under our experimental conditions. The HCl(v) distribution from CH<SUB>3</SUB>COCl is P<SUB>1</SUB>-P<SUB>4</SUB>=39:32:20:9. Surprisal analysis was used to estimate the P<SUB>0</SUB> value as 36% and &lt;&#402;<SUB>v</SUB>(HCl)&gt;=0.12. The reaction time had to be increased from &#8804;0.2 ms to &#8805;0.5 ms to record the HCl(v) emission from F + CH<SUB>2</SUB>COCl, and the best distribution was P<SUB>1</SUB>-P<SUB>4</SUB>+ 68:24:5:3. The estimated ?&#402;v(HCl)? was only 0.06 which is a lower limit due to HCl(v) relaxation. The CO(v =1 &#8594; 0) emission could also be observed from this reaction with an intensity that was typically less than 10% of the HCl(v) emission. Ab initio calculations for FCH<SUB>2</SUB>COCl at MP2/6-31G<SUP>&#x002A;</SUP> level give the threshold energy for HCl elimination as 61 kcal mol<SUP>&#8722;1</SUP>, which is 12 kcal mol<SUP>&#8722;1</SUP> larger than that for CH<SUB>3</SUB>COCl at the same level. The threshold energies for the other reactions of FCH<SUB>2</SUB>COCl are 81.0 for CO elimination, 82.5 for C-C dissociation, and 78.4 for C-Cl dissociation. RRKM and ab initio calculations indicate that CO formation results from the FCH<SUB>2</SUB>COCl &#8594; FCH<SUB>2</SUB>+COCl dissociation step followed by COCl &#8594; CO+ Cl. For CH<SUB>3</SUB>COCl<SUP>&#x002A;</SUP>, with 105 kcal mol<SUP>&#8722;1</SUP> energy, HCl elimination accounts for 98% of the total reaction and C-C dissociation accounts for the rest. The C-Cl dissociation channel is not important for either molecule at these energies