On the choice of explicit stabilizing terms in column generation

Column generation algorithms are instrumental in many areas of applied optimization, where linear programs with an enormous number of columns need to be solved. Although successfully employed in many applications, these approaches suffer from well-known instability issues that somewhat limit their efficiency. Building on the theory developed for nondifferentiable optimization algorithms, a large class of stabilized column generation algorithms can be defined which avoid the instability issues by using an explicit stabilizing term in the dual; this amounts at considering a (generalized) augmented Lagrangian of the primal master problem. Since the theory allows for a great degree of flexibility in the choice and in the management of the stabilizing term, one can use piecewise-linear or quadratic functions that can be efficiently dealt with using off-the-shelf solvers. The practical effectiveness of this approach is demonstrated by extensive computational experiments on large-scale Vehicle and Crew Scheduling problems. Also, the results of a detailed computational study on the impact of the different choices in the stabilization term (shape of the function, parameters), and their relationships with the quality of the initial dual estimates, on the overall effectiveness of the approach are reported, providing practical guidelines for selecting the most appropriate variant in different situations.     

Studies on enaminonitriles: A new synthesis of 1,3‐substituted pyrazole‐4‐carbonitrile

3‐Diethylaminoacrylonitrile ( 1 ) reacts with hydrazonyl halides ( 2a‐d ) to yield 1,3‐disubstituted pyrazole‐4‐carbonitriles 5a‐d. The acetyl 1‐p‐chlorophenylpyrazole‐4‐carbonitrile ( 5a ) condensed with hydrazine hydrate to yield the bishydrazone 10 and with dimethylformamide dimethylacetal to yield 1‐aryl‐3‐(3‐dimethylamino)acryloyl pyrazole‐4‐carbonitrile ( 11 ). This enamine reacts with hydrazine hydrate to yield the pyrazolylpyrazole ( 12 ) and with naphthoquinone to yield the 3‐naphthofuranoyl pyrazole 13. The pyra‐zolyl pyridine derivative 14 was obtained upon treatment of 11 with acetylacetone in the presence of ammonium acetate. Compound 11 was coupled with p‐chlorobenzene diazonium chloride to yield the hydrazone 16 that was coupled further with p‐chlorobenzenediazonium chloride to yield the formazane 18.     

Synthesis and Reactions of 3‐Methylthiazolo[3,2‐a]Benzimidazole‐2‐Carboxylic Acid Hydrazide: Synthesis of Some New Pyrazole, 1,3‐Thiazoline, 1,2,4‐Triazole and 1,2,4‐Triazolo[3,4‐b]‐1,3,4‐Thiadiazine Derivatives Pendant to Thiazolo[3,2‐a]Benzimidazole Moiety

The reaction of 3‐methylthiazolo[3,2‐a]benzimidazole‐2‐carboxylic acid ethyl ester (1) with hydrazine hydrate gives the hydrazide 2 which reacts with CS₂/KOH to afford the potassium salt 3. Treatment of 3 with l‐aryl‐2‐bromoethanones 4a,b afforded the 1,3‐thiazoline derivatives 6a,b, respectively, while the reaction of 3 with hydrazine hydrate afforded 1,2,4‐triazole‐3‐thione derivative 9. The reaction of 9 with l‐aryl‐2‐bromoethanones 4a,b and with hydrazonyl chlorides 11a,b gave the 1,2,4‐triazolo[3,4‐b]‐1,3,4‐thiadiazine derivatives 10a,b and 12a,b, respectively. Treatment of hydrazide 2 with phenyl isothiocyanate in refluxing benzene gave the thiosemicarbazide derivative 16. The latter reaction gave 1,3,4‐oxadiazole derivative 17 when benzene was replaced by DMF. Cyclization of the thiosemicarbazide derivative 16 with NaOH resulted in the formation of the 1,2,4‐triazole‐3‐thione derivative 18.     

Synthesis of some new benzofuran‐based thiophene, 1,3‐oxathiole and 1,3,4‐oxa(thia)diazole derivatives

Treatment of 3‐(3‐methylbenzofuran‐2‐yl)‐3‐oxopropanenitrile ( 1 ) with phenyl isothiocyanate afforded the thioacetanilide derivative 3 , which when reacted with α‐haloketones, α‐halodiketones, and hydrazonoyl chlorides gives thiophene, 1,3‐oxathiole, and 1,3,4‐thiadiazole derivatives 6a,b, 10a,b and 14a–g , respectively. Treatment of 3‐methyl‐2‐benzofurancarboxylic acid hydrazide ( 15 ) with benzaldehyde followed by bromine afforded the 1,3,4‐oxadiazole derivative 18 . Treatment of the acid hydrazide 15 with phenyl isothiocyanate gave the thiosemicarbazide 20 . Compound 20 could be converted into 1,3,4‐oxadiazole, 1,2,4‐triazole‐3‐thione, and 1,3,4‐thiadiazole derivatives 21, 22 , and 23 , respectively. © 2007 Wiley Periodicals, Inc. Heteroatom Chem 18:294–300, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20298     

Synthesis of Some 1,3-Thiazole, 1,3,4-Thiadiazole, Pyrazolo[5,1-c]-1,2,4-triazine, and 1,2,4-Triazolo[5,1-c]-1,2,4-triazine Derivatives Based on the Thiazolo[3,2-a]benzimidazole Moiety

3-(3-Methylthiazolo[3,2-a]benzimidazol-2-yl)-3-oxopropionitrile was synthesized by refluxing ethyl 3-methylthiazolo[3,2-a]benzimidazole-2-carboxylate, acetonitrile, and sodium hydride. Treatment of 3-(3-methylthiazolo[3,2-a]benzimidazol-2-yl)-3-oxopropionitrile with phenyl isothiocyanate, in the presence of KOH, furnished the corresponding potassium salt which was converted into thioacetanilide derivative upon neutralization. The thioacetanilide derivative reacts with α-chloroacetylacetone and ethyl α-chloroacetoacetate to give the 1,3-thiazole derivatives, while the reaction of the'thioacetanilide derivative with hydrazonyl chlorides gave 1,3,4-thiadiazole derivatives. On the other hand, 3-(3-methylthiazolo[3,2-a]benzimidazol-2-yl)-3-oxopropionitrile reacted with the diazonium salt of both 3-phenyl-5-amino-(1H)-pyrazole and 5-amino-l,2,4-(1H)-triazole to afford the corresponding hydrazones. The latter hydrazones underwent an intramolecular cyclization upon boiling in pyridine to give pyrazolo[5,1-c]-1,2,4-triazine and 1,2,4-triazolo[5,1-c]-1,2,4-triazine derivatives. Moreover, the behavior of thiazolo[3,2-a]benzimidazol-3(2H)-one towards phenyl isothiocyanate followed by the reaction with α-chloroketones or hydrazonyl chlorides was investigated. Some of the latter compounds exhibited moderate effects against some bacterial and fungal species.     

Existence and controllability results for impulsive partial functional differential inclusions

In this paper we prove the existence and the controllability of mild and extremal mild solutions for first-order semilinear densely defined impulsive functional differential inclusions in separable Banach spaces with local and nonlocal conditions.     

Lithium sulfate: Calorimetric determination of the temperatures and enthalpies of high-temperature phase transitions

Using a high-temperature Calvet calorimeter as a differential enthalpic analyser Li₂SO₄ was investigated in the temperature range 800–1200 K. One transformation in the solid state was observed at 847 K with a corresponding enthalpy increment of 24.2 kJ mol^?1. The solid-liquid transition was found to occur at 1131 K with an enthalpy of fusion of 7.74 kJ mol^?1. Furthermore, the analysis of the corresponding thermograms supports the presence of the premelting effect which was evidenced by other techniques. A critical comparison with previous results in the literature is given.     

Optimal estimates for blowup rate and behavior for nonlinear heat equations

We first describe all positive bounded solutions of where \input amstex \loadmsbm $(y,s)\in \Bbb R^N\times \Bbb R$ , 1 < p, and (N − 2)p ≤ N + 2. We then obtain for blowup solutions u(t) of uniform estimates at the blowup time and uniform space-time comparison with solutions of u′ = u^p. © 1998 John Wiley & Sons, Inc.