There has been much recent progress in approximation algorithms for nonconvex continuous and discrete problems from both a theoretical and a practical perspective. In discrete (or combinatorial) optimization many approaches have been developed recently that link the discrete universe to the continuous universe through geomet ric, analytic, and algebraic techniques. Such techniques include global optimization formulations, semidefinite programming, and spectral theory. As a result new ap proximate algorithms have been discovered and many new computational approaches have been developed. Similarly, for many continuous nonconvex optimization prob lems, new approximate algorithms have been developed based on semidefinite pro gramming and new randomization techniques. On the other hand, computational complexity, originating from the interactions between computer science and numeri cal optimization, is one of the major theories that have revolutionized the approach to solving optimization problems and to analyzing their intrinsic difficulty. The main focus of complexity is the study of whether existing algorithms are efficient for the solution of problems, and which problems are likely to be tractable. The quest for developing efficient algorithms leads also to elegant general approaches for solving optimization problems, and reveals surprising connections among problems and their solutions. A conference on Approximation and Complexity in Numerical Optimization: Con tinuous and Discrete Problems was held during February 28 to March 2, 1999 at the Center for Applied Optimization of the University of Florida.

Autorentext
Ding-Zhu Du is Professor of Computer Science at the University of Texas at Dallas. For a number of years he was the Editor-in-Chief of the Journal of Combinatorial Optimization and the combinatorial optimization series editor for the SOIA book series. Professor Du is co-editor of the first and second editions of the Handbook of Combinatorial Optimization. He was also co-author (with Pardalos and Wu) of the Kluwer publication "Mathematical Theory of Optimization." Panos M. Pardalos is Distinguished Professor Emeritus of Industrial and Systems Engineering at the University of Florida. Additionally, he is the Paul and Heidi Brown Preeminent Professor in Industrial & Systems Engineering. He is also an affiliated faculty member of the Computer and Information Science Department, the Hellenic Studies Center, and the Biomedical Engineering Program. He is also the Director of the Center for Applied Optimization. Dr. Pardalos is a world leading expert in global and combinatorial optimization. His recent research interests include network design problems, optimization in telecommunications, e-commerce, data mining, biomedical applications, and massive computing. He has co-authored and co-edited more than 30 books, as well as publishing more than 600 journal articles and conference proceedings. Prof. Pardalos is a Fellow of AAAS (American Association for the Advancement of Science), Fellow of American Institute for Medical and Biological Engineering (AIMBE), and EUROPT. He is a Distinguished International Professor by the Chinese Minister of Education; Honorary Professor of Anhui University of Sciences and Technology, China; Elizabeth Wood Dunlevie Honors Term Professor; Honorary Doctor, V.M. Glushkov Institute of Cybernetics of The National Academy of Sciences of Ukraine; Foreign Associate Member of Reial Academia de Doctors, Spain; and Advisory board member of the Centre for Optimisation and Its Applications, Cardiff University, UK. He is also the recipient of UF 2009 International Educator Award; Medal (in recognition of broad contributions in science and engineering) of the University of Catani, Italy; EURO Gold Medal (EGM); Honorary Doctor of Science Degree, Wilfrid Laurier University, Canada; Senior Fulbright Specialist Award; University of Florida Research Foundation Professorship; and IBM Achievement Award.Xiaodong Hu is a research professor at the Institute of Applied Mathematics, Chinese Academy of Sciences. He was the president of OR society of China a few year ago. His research interests include combinatorial optimization, and approximation algorithms, to name just two.Weili Wu is pra ofessor of computer science at the University of Texas at Dallas. Her research interests include optimization theory, big data management and analysis, social networks, database systems, and wireless sensor networks, to name just several. She has published more than200 journal papers and 100 conference papers. Especially, she made several influential contributions in the study of wireless sensor networks, which are accumulated in a Springer publication "Optimal Coverage in Wireless Sensor Networks".

Zusammenfassung
On the other hand, computational complexity, originating from the interactions between computer science and numeri cal optimization, is one of the major theories that have revolutionized the approach to solving optimization problems and to analyzing their intrinsic difficulty.

Inhalt
Navigating Graph Surfaces.- The Steiner Ratio of Lp-planes.- Hamiltonian Cycle Problem via Markov Chains and Min-type Approaches.- Solving Large Scale Uncapacitated Facility Location Problems.- A Branch and Bound Procedure for the Largest Clique in a Graph.- A New Annealed Heuristic for the Maximum Clique Problem.- Inapproximability of some Geometric and Quadratic Optimization Problems.- Convergence Rate of the P-Algorithm for Optimization of Continious Functions.- Application of Semidefinite Programming to Circuit Partitioning.- Combinatorial Problems Arising in Deregulated Electrical Power Industry: Survey and Future Directions.- On Approximating a Scheduling Problem.- Models and Solution for On-Demand Data Delivery Problems.- Complexity and Experimental Evaluation of Primal-Dual Shortest Path Tree Algorithms.- Machine Partitioning and Scheduling under Fault-Tolerance Constraints.- Finding Optimal Boolean Classifiers.- Tighter Bounds on the Performance of First Fit Bin Packing.- Block Exchange in Graph Partitioning.- On the Efficient Approximability of HARD Problems: A Survey.- Exceptional Family of Elements, Feasibility, Solvability and Continuous Paths of ?- Solutions for Nonlinear Complementarity Problems.- Linear Time Approximation Schemes for Shop Scheduling Problems.- On Complexity and Optimization in Emergent Computation.- Beyond Interval Systems: What Is Feasible and What Is Algorithmically Solvable?.- A Lagrangian Relaxation of the Capacitated Multi-Item Lot Sizing Problem Solved with an Interior Point Cutting Plane Algorithm.- An Approximate Algorithm For a Weapon Target Assignment Stochastic Program.- Continuous-based Heuristics for Graph and Tree Isomorphisms, with Application to Computer Vision.- Geometric Optimization Problems forSteiner Minimal Trees in E3.- Optimization of a Simplified Fleet Assignment Problem with Metaheuristics: Simulated Annealing and GRASP.- Towards Implementations of Successive Convex Relaxation Methods for Nonconvex Quadratic Optimization Problems.- Piecewise Concavity and Discrete Approaches to Continuous Minimax Problems.- The MCCNF Problem with a Fixed Number of Nonlinear Arc Costs: Complexity and Approximation.- A New Parametrization Algorithm for the Linear Complementarity Problem.- Obtaining an Approximate Solution for Quadratic Maximization Problems.