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.
This collection of literature attempts to compile many of the classic works that have stood the test of time and offer them at a reduced, affordable price, in an attractive volume so that everyone can enjoy them.
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).
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