We study the numerical performance of a limited memory quasi Newton method for large scale optimization which we call the L BFGS method We compare its performance with that of the method developed by Buckley and LeNir which combines cyles of BFGS steps and conjugate direction steps Our numerical tests indicate that the L BFGS method is faster than the method of Buckley and LeNir and is better a...

We study the numerical performance of a limited memory quasi-Newton method for large scale optimization, which we call the L-BFGS method. We compare its performance with that of the method developed by Buckley and LeNir (1985), which combines cyles of BFGS steps and conjugate direction steps. Our numerical tests indicate that the L-BFGS method is faster than the method of Buckley and LeNir, and...

Professor Frank Harary has had a singular influence on graph theory through his own extensive original research, through the training of several researchers who themselves have made many important contributions, and through popularizing work, most significantly his text Graph Theory [1]. Frank Harary has contributed to a number of more advanced specialized texts, like that of Buckley and Harary...

We present analytical solutions for capillary-controlled displacement in one dimension by use of fractional-flow theory. We show how to construct solutions with a spreadsheet that can be used for the analysis of experiments as well as matrix-block-scale recovery in field settings. The solutions can be understood as the capillary analog to the classical Buckley-Leverett solution (Buckley and Lev...

For the hyperbolic conservation laws with discontinuous flux function there may exist several consistent notions of entropy solutions; the difference between them lies in the choice of the coupling across the flux discontinuity interface. In the context of Buckley-Leverett equations, each notion of solution is uniquely determined by the choice of a “connection”, which is the unique stationary s...

Choosing a supplier is complex decision-making process that can reduce the total cost of production inputs and increase profits without increasing price or sacrificing product quality. However, selection processes usually involve multiple quantitative qualitative criteria which complexity problem may decrease accuracy effectiveness process. Such problems be supported by using multicriteria (MCD...