Convergence of interval-type algorithms for generalized fractional programming

The purpose of this paper is to analyze the convergence of interval-type algorithms for solving the generalized fractional program. They are characterized by an interval [LB _k , UB _k ] including*, and the length of the interval is reduced at each iteration. A closer analysis of the bounds LB _k and UB _k allows to modify slightly the best known interval-type algorithm NEWMODM accordingly to prove its convergence and derive convergence rates similar to those for a Dinkelbach-type algorithm MAXMODM under the same conditions. Numerical results in the linear case indicate that the modifications to get convergence results are not obtained at the expense of the numerical efficiency since the modified version BFII is as efficient as NEWMODM and more efficient than MAXMODM.This research was supported by NSERC (Grant A8312) and FCAR (Grant 0899).     

Algorithms for generalized fractional programming

A generalized fractional programming problem is specified as a nonlinear program where a nonlinear function defined as the maximum over several ratios of functions is to be minimized on a feasible domain of ⁿ . The purpose of this paper is to outline basic approaches and basic types of algorithms available to deal with this problem and to review their convergence analysis. The conclusion includes results and comments on the numerical efficiency of these algorithms.This research was supported by NSERC (grant A8312) and Cooperation franco-québécoise (projet 20-02-13). Paper presented at Workshop on Mathematical Programming Catholic University of Rio de Janeiro, Brazil, October 10–14, 1988.     

Clustering for routing in densely populated areas

This paper introduces a new approach for generating school bus routes in a dense urban area. First, a districting algorithm is used to determine clusters including appropriate numbers of students. Then, for each cluster, a route and the stops along this route are determined. Numerical results are reported and compared with those obtained previously. Although the algorithm has been developped and tested in a specific context, it could easily be extended to more general vehicle routing problems.     

Measurement of filament length generated by an intense femtosecond laser pulse using electromagnetic radiation detection

We present a new method to measure the length of a filament induced by the propagation of intense femtosecond laser pulses in air. We used an antenna to detect electromagnetic pulses radiated from multipole moments inside the filament oscillating at the plasma frequency. The results are compared with the values detected from the backscattered fluorescence induced by multiphoton ionization of nitrogen molecules excited inside the filament. The values are found to be in good agreement. Received: 6 November 2002 / Revised version: 27 January 2003 / Published online: 24 April 2003 RID="*" ID="*"Corresponding author. Fax: +1-418/656-2623, E-mail: shosseini@phy.ulaval.ca     

A note on an algorithm for generalized fractional programs

We present a modification of an algorithm recently suggested by the same authors in this journal (Ref. 1). The speed of convergence is improved for the same complexity of computation.The research of S. Schaible was supported by Grants A4534 and A5408 from NSERC.     

Generalized fractional programming: Algorithms and numerical experimentation

Several algorithms to solve the generalized fractional program are summarized and compared numerically in the linear case. These algorithms are iterative procedures requiring the solution of a linear programming problem at each iteration in the linear case. The most efficient algorithm is obtained by marrying the Newton approach within the Dinkelbach approach for fractional programming.     

Matrix criteria for pseudo-convex functions in the class C2

This paper establishes the relations existing between two sets of conditions for the pseudo-convexity of functions in the class C² determined by Mereau and Paquet and by the author, respectively.     

RCM of tripeptide dienes containing a chiral vinylcyclopropane moiety: impact of different Ru-based catalysts on the stereochemical integrity of the macrocyclic products

[structures: see text] Tripeptide dienes containing an (1R,2S)-vinyl aminocyclopropylcarboxylate residue were cyclized to beta-strand scaffolds under ring-closing metathesis (RCM). Conformational factors, ligand effects, and reaction conditions were evaluated. A protocol was developed for the efficient synthesis of 15-membered ring peptides in high diastereomeric purity. These peptides are key synthetic precursors to antiviral agents that target the hepatitis C virus and represent the first class of clinically validated pharmaceutical agents that are synthesized in large scale using RCM.