There is a growing need in major industries such as airline, trucking, financial engineering, etc. to solve very large linear and integer linear optimization problems. Because of the dramatic increase in computing power, it is now possible to solve these problems. Along with the increase in computer power, the mathematical programming community has developed better and more powerful algorithms to solve very large problems. These algorithms are of interest to many researchers in the areas of operations research/management science, computer science, and engineering. In this book, Kipp Martin has systematically provided users with a unified treatment of the algorithms and the implementation of the algorithms that are important in solving large problems.
Combinatorial (or discrete) optimization is one of the most active fields in the interface of operations research, computer science, and applied math- ematics. Combinatorial optimization problems arise in various applications, including communications network design, VLSI design, machine vision, air- line crew scheduling, corporate planning, computer-aided design and man- ufacturing, database query design, cellular telephone frequency assignment, constraint directed reasoning, and computational biology. Furthermore, combinatorial optimization problems occur in many diverse areas such as linear and integer programming, graph theory, artificial intelligence, and number theory. All these problems, when formulated mathematically as the minimization or maximization of a certain function defined on some domain, have a commonality of discreteness. Historically, combinatorial optimization starts with linear programming. Linear programming has an entire range of important applications including production planning and distribution, personnel assignment, finance, alloca- tion of economic resources, circuit simulation, and control systems. Leonid Kantorovich and Tjalling Koopmans received the Nobel Prize (1975) for their work on the optimal allocation of resources. Two important discover- ies, the ellipsoid method (1979) and interior point approaches (1984) both provide polynomial time algorithms for linear programming. These algo- rithms have had a profound effect in combinatorial optimization. Many polynomial-time solvable combinatorial optimization problems are special cases of linear programming (e.g. matching and maximum flow). In addi- tion, linear programming relaxations are often the basis for many approxi- mation algorithms for solving NP-hard problems (e.g. dual heuristics).
This volume contains the proceedings of the workshop on Optimization Theory and Related Topics, held in memory of Dan Butnariu, from January 11-14, 2010, in Haifa, Israel. An active researcher in various fields of applied mathematics, Butnariu published over 80 papers. His extensive bibliography is included in this volume. The articles in this volume cover many different areas of Optimization Theory and its applications: maximal monotone operators, sensitivity estimates via Lyapunov functions, inverse Newton transforms, infinite-horizon Pontryagin principles, singular optimal control problems with state delays, descent methods for mixed variational inequalities, games on MV-algebras, ergodic convergence in subgradient optimization, applications to economics and technology planning, the exact penalty property in constrained optimization, nonsmooth inverse problems, Bregman distances, retraction methods in Banach spaces, and iterative methods for solving equilibrium problems. This volume will be of interest to both graduate students and research mathematicians.
"Vol 30-A": The collection includes both refereed articles and review essays of recently published books in the history of economic thought and methodology. The articles highlight the work of founding editor Warren J. Samuels, American economists' role in the creation of federal trade acts, and Islamic economic methodology. A review symposium on Malcolm Rutherford's "The Insitutionalist Movement in America" is followed by reviews of books on Adam Smith, George Warde Norman, William Whewell and Richard Jones, J.S. Mill and F.A. Hayek. "Vol 30-B": This volume includes archival documents and essays exploring the inter-relationship between the government and the economy. Levy, Peart, and Albert examine the one-sided controversy generated by Rose Wilder Lane and V. Orval Watts against a new generation of Keynes-influenced textbooks focused on governmental policy and the scope of government activity. Warren J. Samuels examines Heinrich von Treitschke's view on property as a function of politics using archival documents. Also included is a detailed examination of Warren J. Samuels' views on the economic role of government, as well as two sets of course notes in addition to the introductory essay.
Aphids are the most important of the sap sucking insects, they are also major pests of agriculture, horticulture and forestry. This book covers the evolution of aphids and their development in relation to specific plants. Optimization is used to explain how modes of feeding and reproduction have affected their size and population structure and led to a very close and specific association with their host plants.
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