Approximation and Complexity in Numerical Optimization

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.

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.