grams of which the objective is given by the ratio of a convex by a positive (over a convex domain) concave function. As observed by Sniedovich (Ref. [102, 103]) most of the properties of fractional proÂ grams could be found in other programs, given that the objective function could be written as a particular composition of functions. He called this new field CÂ programming, standing for composite concave programming. In his seminal book on dynamic programming (Ref. ), Sniedovich shows how the study of such comÂ positions can help tackling non-separable dynamic programs that otherwise would defeat solution. Barros and Frenk (Ref. ) developed a cutting plane algorithm capable of optimizing C-programs. More recently, this algorithm has been used by Carrizosa and Plastria to solve a global optimization problem in facility location (Ref. ). The distinction between global optimization problems (Ref. ) and generalized convex problems can sometimes be hard to establish. That is exactly the reason why so much effort has been placed into finding an exhaustive classification of the different weak forms of convexity, establishing a new definition just to satisfy some desirable property in the most general way possible. This book does not aim at all the subtleties of the different generalizations of convexity, but concentrates on the most general of them all, quasiconvex programming. Chapter 5 shows clearly where the real difficulties appear.
Collocation is an important tool in describing lexical behaviour in language and has received increasing attention in recent years. Based on two corpora: LOCNESS (the Louvain Corpus of Native English Essays) and MLC (the Non-English major Mainland Chinese Learner Corpus), this book explores the features of Chinese learner English with analysis of grammatical and lexical collocations. The findings show that Chinese university students use collocations with considerably less variety and Chinese language and culture exert a substantial influence on their English writing. It also discusses ways to tackle the problems Chinese English learners face and the pedagogical implications for teaching English and learning English collocations. As one of the first systematic studies to investigate collocations in Chinese learner English based on learner corpora, this book not only analyzes how Chinese learners use collocations in their English writing, but also provides significant implications for foreign language teaching and learning.
Three different lines of approach have contributed to the theory of optimal planning. One approach considers the problem from the view-point of a national government and its adviser, the econometrician planning speciÂ alist. The government can, if this is thought to be desirable, stimulate investment in certain directions and discourage other economic activities. By various fiscal devices, it can influence both the total level and the distribution of investment funds over different sectors of production. Also, in many countries, a public agency plays some kind of coordinatÂ ing role in the formulation of long-term plans for output by the enterÂ prises sector; this may range from administrative direction in so-called centrally planned economies, to persuasion and advice in 'capitalist' economies. Accordingly, the public planner wishes to know what disÂ tribution of the nation's resources would be 'optimal'. This leads to the construction of various models which may be described under the general heading 'input-output type models'. This type of model has been largely developed by practitioners, among whom Sandee [B2] is probably the most outstanding and the earliest. A later, well-developed example of a model based on this approach is, for example, the Czech model by Cerny et al. [Bl]. A second approach considers the problem from the point of view of the private entrepreneur and his adviser, the manager and financial accountant.
Sebel Hawkesbury Articles
Sebel Hawkesbury Books