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Packing and vehicle routing problems play an important role in the area of supply chain management. In this paper, we introduce a non-linear knapsack problem that occurs when packing items along a fixed route and taking into account travel time. We investigate constrained and unconstrained versions of the problem and show that both are NP-hard. In order to solve the problems, we provide a pre-processing scheme as well as exact and approximate mixed integer programming (MIP) solutions. Our experimental results show the effectiveness of the MIP solutions and in particular point out that the approximate MIP approach often leads to near optimal results within far less computation time than the exact approach.

The paper discusses duality for linear and nonlinear programs in which some of the variables are arbitrarily constrained. The most important class of such problems is that of mixed-integer (linear and nonlinear) programs. The paper introduces the duality constructions and discusses algorithms based on them.

Bibliography: leaves 48-49

In this paper, we mainly study one class of convex mixed-integer nonlinear programming problems (MINLPs) with non-differentiable data. By dropping the differentiability assumption, we substitute gradients with subgradients obtained from KKT conditions, and use the outer approximation method to reformulate convex MINLP as one equivalent MILP master program. By solving a finite sequence of subproblems and relaxed MILP problems, we establish an outer approximation algorithm to find the optimal solution of this convex MINLP. The convergence of this algorithm is also presented. The work of this paper generalizes and extends the outer approximation method in the sense of dealing with convex MINLPs from differentiable case to non-differentiable one.

LibriVox volunteers bring you 14 recordings of <em>Convention</em> by Agnes Lee. This was the weekly poetry project for December 21st, 2008.

<i>A Phantom Lover</i> is a supernatural novella by Vernon Lee (pseudonym of Violet Paget) first published in 1886. Set in a Kentish manor house, the story concerns a portrait painter commissioned by a squire, William Oke, to produce portraits of him and his wife, the eccentric Mrs. Alice Oke, who bears a striking resemblance to a woman in a mysterious, seventeenth century painting. (Summary by Anthony Leslie)

<p>An early example of the female private detective, Jennette Lee’s Millicent Newberry made her first appearance in The Green Jacket in 1917 and was also featured in two later books, The Mysterious Office in 1922 and Dead Right in 1925. Miss Newberry brings her own unique perspective to her cases, only accepting those where she has a say in what happens to the guilty party. She is rarely without her knitting, using it as a technique to put clients and suspects alike at ease, while also knitting her notes on the case into the pattern! In The Green Jacket, Millie goes undercover to solve a case involving a stolen emerald necklace that, despite the efforts of other detectives, including her former boss, Tom Corbett, has never been recovered. (Summary by J. M. Smallheer)

4Lost Art of Reading

By Gerald Stanley Lee

Gerald Stanley Lee speaks here-in of books and self in the time of factories, tall buildings and industry and big city making, the effects of modern civilization on the individual. - Summary by Joseph Tabler

5Anecdotes of the Habits and Instinct of Animals

By Mrs. Robert Lee

Stories about unusual interactions between animals and humans that reflect some attitudes to the wild in the mid-eighteen hundreds, including trophy hunting.<br><br>"Chronically ill and often in pain," the author, Mary Custis Lee, experienced "hardship with sturdy and radiant faith." Maybe that's why she did not turn away in this book, from unpleasant and often gory accounts of animal encounters. (Summary by Czandra)

6Hauntings

By Vernon Lee

"Hence, my four little tales are of no genuine ghosts in the scientific sense; they tell of no hauntings such as could be contributed by the Society for Psychical Research, of no specters that can be caught in definite places and made to dictate judicial evidence. My ghosts are what you call spurious ghosts (according to me the only genuine ones), of whom I can affirm only one thing, that they haunted certain brains, and have haunted, among others, my own and my friends'—yours, dear Arthur Lemon, along the dim twilit tracks, among the high growing bracken and the spectral pines, of the south country; and yours, amidst the mist of moonbeams and olive-branches, dear Flora Priestley, while the moonlit sea moaned and rattled against the moldering walls of the house whence Shelley set sail for eternity." (Summary by Vernon Lee from the Preface)

Muna Lee was a poet, novelist, translator and activist. This collection, first published in 1923, explores themes of love and place. - Summary by Newgatenovelist