Solving nonlinear multicommodity flow problems by the analytic center cutting plane method

The paper deals with nonlinear multicommodity flow problems with convex costs. A decomposition method is proposed to solve them. The approach applies a potential reduction algorithm to solve the master problem approximately and a column generation technique to define a sequence of primal linear programming problems. Each subproblem consists of finding a minimum cost flow between an origin and a destination node in an uncapacited network. It is thus formulated as a shortest path problem and solved with Dijkstra's d-heap algorithm. An implementation is described that takes full advantage of the supersparsity of the network in the linear algebra operations. Computational results show the efficiency of this approach on well-known nondifferentiable problems and also large scale randomly generated problems (up to 1000 arcs and 5000 commodities

Nonsmooth Optimization; Proceedings of an IIASA Workshop, March 28 - April 8, 1977

Optimization, a central methodological tool of systems analysis, is used in many of IIASA's research areas, including the Energy Systems and Food and Agriculture Programs. IIASA's activity in the field of optimization is strongly connected with nonsmooth or nondifferentiable extreme problems, which consist of searching for conditional or unconditional minima of functions that, due to their complicated internal structure, have no continuous derivatives. Particularly significant for these kinds of extreme problems in systems analysis is the strong link between nonsmooth or nondifferentiable optimization and the decomposition approach to large-scale programming. This volume contains the report of the IIASA workshop held from March 28 to April 8, 1977, entitled Nondifferentiable Optimization. However, the title was changed to Nonsmooth Optimization for publication of this volume as we are concerned not only with optimization without derivatives, but also with problems having functions for which gradients exist almost everywhere but are not continous, so that the usual gradient-based methods fail. Because of the small number of participants and the unusual length of the workshop, a substantial exchange of information was possible. As a result, details of the main developments in nonsmooth optimization are summarized in this volume, which might also be considered a guide for inexperienced users. Eight papers are presented: three on subgradient optimization, four on descent methods, and one on applicability. The report also includes a set of nonsmooth optimization test problems and a comprehensive bibliography

Generalized convexities and semismoothness of nonsmooth functions

This paper discusses generalizations of convexities for nonsmooth functions, or functions that are not continuously differentiable. The paper starts with some basic definitions of group theory. Next we define a convex set and a convex function and discuss some of their properties. We examine the relation between a convex set and a convex function and define a locally Lipschitz continuous function. After that we discuss the optimization of a convex function. For this we define the subgradient of a function and prove a condition concerning the subgradient which is used to find the minimum of a convex function. In the next chapter we discuss nonsmooth and nonconvex functions. For these functions we define the Clarke generalized directional derivative and go through some of its properties. The generalized subgradient is used to define the generalized subgradient of a function. Next we define pseudo- and quasiconvexity for nonsmooth functions by using the Clarke generalized directional derivative. We also go through the relations between convexities and the optimality conditions of smooth and nonsmooth functions. In the final chapter we define different kinds of semismooth functions and go through their relations between convex and generalized convex functions. We also define functions whose generalized directional derivative is well-behaved and show an important connection between well-behaved functions and generalized convexities

Derivative free algorithms for nonsmooth and global optimization with application in cluster analysis

This thesis is devoted to the development of algorithms for solving nonsmooth nonconvex problems. Some of these algorithms are derivative free methods.Doctor of Philosoph

Contribution à l'optimisation non-différentiable et à la décomposition en programmation mathématique

Le problème : définition et quelques cas particuliers -- Travaux apparentés -- Accélération et stabilisation des algorithmes de plans sécants en programmation mathématique convexe -- Construction et mise-à-jour des problèmes de recherche d'une somme de fonctions convexes -- Un algorithme de descente pour la minimisation d'une somme de fonctions convexes -- Expérimentation numérique

Progress in Nondifferentiable Optimization

This volume grew out of the second meeting on nondifferentiable optimization, a field whose most important applications lie in treating problems of decision-making under uncertainty. Since the first meeting, held in 1977, new results were obtained in the theory of optimality conditions, and there was more understanding of the relationships between various classes of nondifferentiable functions. All of these new developments were discussed at the meeting, the reports presented by the participants covering the theory of generalized differentiability, optimality conditions, and the numerical testing and applications of algorithms. After the meeting the participants prepared extended versions of their contributions; these revised papers form the core of this volume, which also contains a bibliography of over 300 references to published work on nondifferentiable optimization, prepared by the editor

Barbed bone and antler technologies: cultural transmission and variation in the Gulf of Georgia, Northwest North America

Although archaeologists have long discussed the evolution of the social stratification and complex group interactions of the hunter-gatherer-fishers of the Northwest Coast (e.g. Matson and Coupland 1994; Ames 1994), few have examined the implied interactions between material culture and the development of complexity in the Gulf of Georgia postulated to have occurred approximately 2600 years ago. When viewed from a Darwinian perspective, specifically Boyd and Richerson\u27s (1985) dual inheritance theory, the development of social stratification and systems of deference may influence the contexts of social learning. I hypothesize that prestige bias (Henrich and Henrich 2007) emerged as a factor in the social learning of technologies tied to systems of resource procurement and prestige-based status, as complexity developed. Barbed bone and antler points are examined in this analysis as a technology tied to these resource systems and prestige-based status. A total of 593 artifacts were examined from 56 archaeological sites from the collections at Western Washington University, the Burke Museum, the Royal British Columbia Museum, and Simon Fraser University. McMurdo\u27s (1972) typology was used as a basis for the examination of attributes. Cladistics was employed using models developed by Eerkens and his coauthors. (2006) in order to detect prestige bias, represented by a branching phylogeny of descent with modification as opposed to a stochastic pattern. Dunnell\u27s (1978) definition of stylistic and functional traits coupled with cluster analyses were utilized in the examination of attributes to select traits that would not result in a \u27false\u27 phylogenetic signal due to artifact functional constraints. In addition to examining the cultural transmission of barbed bone and antler points, the data set was also used to assess previous interpretations of artifact function (e.g. Carlson 1954). Four functional classes (retrievable points, fixed points, leisters, fish hooks) were constructed for this purpose and to determine if there were distinctions in metric attributes between classes. Variation within fixed points was also examined to determine if there were detectable distinctions in attributes hypothesized to be linked to functions such as a fish spears or arrow points (e.g. Carlson 1954, Clark 1975) such as barb morphology, crosssection, and base length. The cultural-historical significance of attributes such as the transition from bilateral to unilateral barb application and line attachments through time and the trend towards squared, enclosed, barbs in later periods were also assessed (Drucker 1943; McMurdo 1972). Cladistics analysis, using geographically and chronologically outlying assemblages as an outgroup, revealed a stochastic pattern of cultural transmission, implying highly individualized (guided variation) or peer based learning (horizontal transmission) rather than prestige bias. Cluster analyses demonstrate considerable geographic homogeneity in the morphological attributes of barbed points, indicating that similar barbed point styles were present throughout the Gulf of Georgia over the past 3500 years. Barb morphological attributes, as indicated by the frequencies of barb paradigmatic classes, also demonstrate considerable continuity over the past 3500 years. Clear distinctions were detected in the metric attributes of morphologically defined functional classes. Variation in the morphology of fixed points, indicative of possible function as a fish spear or bird arrow was also detected. Attributes McMurdo (1972) argued had culture-historic significance, with the exception of those tied to barb morphology, were found to be chronologically sensitive

Interdisciplinary Approach to Liquid Lubricant Technology

The proceedings of a conference of liquid lubricant technology are presented. The subjects discussed are: (1) requirements and functions of liquid lubricants, (2) mineral oils, (3) greases, (4) theory of rheology, (5) mechanics and thermodynamics in lubrication, (6) environmental capability of liquid lubricants, and (7) wear corrosion and erosion