Ideal points in multiobjective programming

The main object of this paper is to give conditions under which a minimal solution to a problem of mathematical programming can be transformed into a minimum solution in the usual sense of the order relations, or in every case, conditions under which that solution is adherent to the set of the points wich verify this last property. The interest of this problem is clear, since many of the usual properties in optimization (like, for instance, the analysis of the sensitivity of the solutions) are studied more easily for minimum solutions than for minimal solutions

Sensitivity Analysis for Convex Multiobjective Programming in Abstract Spaces.

The main object of this paper is to prove that for a linear or convex multiobjective program, a dual program can be obtained which gives the primal sensitivity without any special hypothesis about the way of choosing the optimal solution in the efficient set.

Existence of solutions for vector optimization

AbstractIn this paper, we prove the existence of a weak minimum for constrained vector optimization problem by making use of vector variational-like inequality and preinvex functions

AFRICAN AMERICAN ENVIRONMENTAL ETHICS: BLACK INTELLECTUAL PERSPECTIVES 1850-1965

The historical scholarship in environmental history centers around the narratives of elite white men. Therefore, scholars such as William Cronon, Dorceta Taylor, Noël Sturgeon, and Carolyn Merchant are calling for research that uncovers the political and moral stances of people of color on nature, land ownership, and environmental pollution. This dissertation addresses this call by engaging William H. Sewell Jr.’s cross-disciplinary approach between history and the social sciences to introduce a nuanced historical analysis that interrogates the channels via which African Americans’ environmental ethic sculpted the development of North American environmental history and activism. This dissertation contends that African Americans interjected a social justice component to environmental activism. Through analyzing government documents, military records, archival documents, oral histories conducted in several states, literary works, diaries, newspapers, Court opinions, religious doctrine, archaeological research, and speeches, this study examines how the natural environment fashioned African Americans’ direct forms of activism against institutionalized slavery, a failed Reconstruction, collapsed economy during the Great Depression, and forced ghettoized living conditions in urban spaces spurred by racial restrictive covenants during the 20th century. These forms of activism include but are not limited to the Negro Spirituals, marronage, institutional educational centers like Tuskegee and Hampton Normal Institute, Southern Tenant Farmers’ Union (STFU), New Negro Harlem Renaissance Movement, civil litigation, and the Black Arts Movement. This work will usher a new discourse in environmental history and bring African Americans into the transnational environmental dialogue

Topics in optimization.

Song, Haifeng.Thesis (M.Phil.)--Chinese University of Hong Kong, 2009.Includes bibliographical references (leaves 67-69).Abstract also in Chinese.Chapter 1 --- Introduction --- p.5Chapter 2 --- Preliminary --- p.8Chapter 2.1 --- Introduction --- p.8Chapter 2.2 --- Notations and fundamental properties --- p.8Chapter 2.3 --- Properties of polyhedra --- p.14Chapter 3 --- Results on Efficient Point Sets --- p.23Chapter 3.1 --- Introduction --- p.23Chapter 3.2 --- Geometric results on efficient point sets --- p.24Chapter 3.3 --- Density of positive proper efficient point sets --- p.33Chapter 4 --- Pareto Solutions of Polyhedral-valued Vector Optimization --- p.42Chapter 4.1 --- Introduction --- p.42Chapter 4.2 --- The structure of weak Pareto solution sets --- p.43Chapter 4.2.1 --- The general ordering cone case --- p.46Chapter 4.2.2 --- The polyhedral ordering cone case --- p.54Chapter 4.3 --- Connectedness of solution sets and optimal value sets --- p.55Chapter 4.4 --- Optimality conditions of piecewise linear mappings --- p.60Bibliography --- p.6

Non-linear functional analysis and vector optimization.

by Yan Shing.Thesis (M.Phil.)--Chinese University of Hong Kong, 1999.Includes bibliographical references (leaves 78-80).Abstract also in Chinese.Chapter 1 --- Admissible Points of Convex Sets --- p.7Chapter 1.1 --- Introduction and Notations --- p.7Chapter 1.2 --- The Main Result --- p.7Chapter 1.2.1 --- The Proof of Theoreml.2.1 --- p.8Chapter 1.3 --- An Application --- p.10Chapter 2 --- A Generalization on The Theorems of Admissible Points --- p.12Chapter 2.1 --- Introduction and Notations --- p.12Chapter 2.2 --- Fundamental Lemmas --- p.14Chapter 2.3 --- The Main Result --- p.16Chapter 3 --- Introduction to Variational Inequalities --- p.21Chapter 3.1 --- Variational Inequalities in Finite Dimensional Space --- p.21Chapter 3.2 --- Problems Which Relate to Variational Inequalities --- p.25Chapter 3.3 --- Some Variations on Variational Inequality --- p.28Chapter 3.4 --- The Vector Variational Inequality Problem and Its Relation with The Vector Optimization Problem --- p.29Chapter 3.5 --- Variational Inequalities in Hilbert Space --- p.31Chapter 4 --- Vector Variational Inequalities --- p.36Chapter 4.1 --- Preliminaries --- p.36Chapter 4.2 --- Notations --- p.37Chapter 4.3 --- Existence Results of Vector Variational Inequality --- p.38Chapter 5 --- The Generalized Quasi-Variational Inequalities --- p.44Chapter 5.1 --- Introduction --- p.44Chapter 5.2 --- Properties of The Class F0 --- p.46Chapter 5.3 --- Main Theorem --- p.53Chapter 5.4 --- Remarks --- p.58Chapter 6 --- A set-valued open mapping theorem and related re- sults --- p.61Chapter 6.1 --- Introduction and Notations --- p.61Chapter 6.2 --- An Open Mapping Theorem --- p.62Chapter 6.3 --- Main Result --- p.63Chapter 6.4 --- An Application on Ordered Normed Spaces --- p.66Chapter 6.5 --- An Application on Open Decomposition --- p.70Chapter 6.6 --- An Application on Continuous Mappings from Order- infrabarreled Spaces --- p.72Bibliograph

Un método símplex en programación lineal multiobjetivo

En este Trabajo Final de Grado se estudia el algoritmo símplex multiobjetivo propuesto por Ehrgot en [1] para calcular las soluciones eficientes de un problema de optimización lineal multiobjetivo. El Capítulo 1 contiene de forma resumida el conocido método símplex introducido por Dantzig en 1947 para resolver problemas de optimización lineales. Además del algoritmo símplex y su variante de las dos fases, se estudian resultados y definiciones de programación lineal que luego serán utilizados para el método símplex que se expondrá en el Capítulo 3. En el Capítulo 2, se hace una introducción a los problemas de optimización mulitobjetivo, es decir, problemas donde se tiene más de una función para optimizar simultáneamente. Se muestra que los puntos eficientes son las "soluciones" de este tipo de problemas y los puntos no dominados son lo análogo a los valores óptimos de las funciones objetivo en los problemas de optimización uniobjetivo. También se explica el método escalar de suma ponderada que permite resolver problemas de optimización multiobjetivo resolviendo en su lugar uno con un solo objetivo. Este capítulo concluye con la exposición de otros métodos para resolver problemas de optimización multiobjetivo entre los que destaca el método de Benson. En el Capítulo 3 se estudian los problemas de optimización lineales multiobjetivo. Tras definir este tipo de problemas y sus puntos eficientes y no dominados, se introducen y demuestran los principales teoremas que permiten justificar el método símplex multiobjetivo. Se explicará el algoritmo símplex multiobjetivo que permite calcular las soluciones eficientes básicas de un problema de optimización lineal multiobjetivo. Este algoritmo se basa en tres fases. En la primera se determina si el problema es o no factible, si es factible, en la segunda fase se determina si el conjunto de puntos eficientes es vacío o no. Por último, si el conjunto de puntos eficientes no es vacío se calculan todas las bases eficientes para caracterizar dicho conjunto. También se ve un ejemplo de resolución de un problema mediante el uso de dicho algoritmo. Por último, en el Capítulo 4 se implementa el algoritmo símplex multiobjetivo con el sofware Xpress. Se comprueba su funcionamiento con varios problemas test y se exponen las conclusiones de dichas pruebas.Grado en Matemática

On generalizations of the Arrow-Barankin-Blackwell Theorem in vector optimization.

Chan Ka Wo.Thesis (M.Phil.)--Chinese University of Hong Kong, 2000.Includes bibliographical references (leaves 114-118).Abstracts in English and Chinese.Introduction --- p.iiiConventions of This Thesis --- p.viPrerequisites --- p.xiiiChapter 1 --- Cones in Real Vector Spaces --- p.1Chapter 1.1 --- The Fundamentals of Cones --- p.2Chapter 1.2 --- Enlargements of a Cone --- p.22Chapter 1.3 --- Special Cones in Real Vector Spaces --- p.29Chapter 1.3.1 --- Positive Cones --- p.29Chapter 1.3.2 --- Bishop-Phelps Cones --- p.36Chapter 1.3.3 --- Quasi-Bishop-Phelps Cones --- p.42Chapter 1.3.4 --- Quasi*-Bishop-Phelps Cones --- p.45Chapter 1.3.5 --- Gallagher-Saleh D-cones --- p.47Chapter 2 --- Generalizations in Topological Vector Spaces --- p.52Chapter 2.1 --- Efficiency and Positive Proper Efficiency --- p.54Chapter 2.2 --- Type I Generalizations --- p.71Chapter 2.3 --- Type II Generalizations --- p.82Chapter 2.4 --- Type III Generalizations --- p.92Chapter 3 --- Generalizations in Dual Spaces --- p.97Chapter 3.1 --- Weak*-Support Points of a Set --- p.98Chapter 3.2 --- Generalizations in the Dual Space of a General Normed Space --- p.100Chapter 3.3 --- Generalizations in the Dual Space of a Banach Space --- p.104Epilogue: Glimpses Beyond --- p.112Bibliography --- p.11