Ebook: Approximation and Complexity in Numerical Optimization: Continuous and Discrete Problems

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.

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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 geometric, analytic, and algebraic techniques. Such techniques include global optimization formulations, semidefinite programming, and spectral theory. As a result new approximate algorithms have been discovered and many new computational approaches have been developed. Similarly, for many continuous nonconvex optimization problems, new approximate algorithms have been developed based on semidefinite programming and new randomization techniques. On the other hand, computational complexity, originating from the interactions between computer science and numerical 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. The two themes of approximation and complexity pervade this book.
Audience: Faculty, graduate students, and researchers in mathematical programming, computer sciences and engineering.

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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 geometric, analytic, and algebraic techniques. Such techniques include global optimization formulations, semidefinite programming, and spectral theory. As a result new approximate algorithms have been discovered and many new computational approaches have been developed. Similarly, for many continuous nonconvex optimization problems, new approximate algorithms have been developed based on semidefinite programming and new randomization techniques. On the other hand, computational complexity, originating from the interactions between computer science and numerical 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. The two themes of approximation and complexity pervade this book.
Audience: Faculty, graduate students, and researchers in mathematical programming, computer sciences and engineering.
Content:
Front Matter....Pages i-xvii
Navigating Graph Surfaces....Pages 1-16
Hamiltonian Cycle Problem via Markov Chains and Min-type Approaches....Pages 17-30
Solving Large Scale Uncapacitated Facility Location Problems....Pages 31-47
A Branch-and-Bound Procedure for the Largest Clique in a Graph....Pages 48-62
A New “Annealed” Heuristic for the Maximum Clique Problem....Pages 63-77
Inapproximability of some Geometric and Quadratic Optimization Problems....Pages 78-95
Convergence Rate of the P-Algorithm for Optimization of Continuous Functions....Pages 96-115
Application of Semidefinite Programming to Circuit Partitioning....Pages 116-129
Combinatorial Problems Arising in Deregulated Electrical Power Industry: Survey and Future Directions....Pages 130-137
On Approximating a Scheduling Problem....Pages 138-162
Models and Solution for On-Demand Data Delivery Problems....Pages 163-174
Complexity and experimental evaluation of primal-dual shortest path tree algorithms....Pages 175-188
Machine Partitioning and Scheduling under Fault-Tolerance Constraints....Pages 189-208
Finding Optimal Boolean Classifiers....Pages 209-244
Tighter Bounds on the Performance of First Fit Bin Packing....Pages 245-286
Block Exchange in Graph Partitioning....Pages 287-297
On the Efficient Approximability of “HARD” Problems: A Survey....Pages 298-307
Exceptional Family of Elements, Feasibility, Solvability and Continuous Paths of ?-Solutions for Nonlinear Complementarity Problems....Pages 308-322
Linear Time Approximation Schemes for Shop Scheduling Problems....Pages 323-337
On Complexity and Optimization in Emergent Computation....Pages 338-346
Beyond Interval Systems: What Is Feasible and What Is Algorithmically Solvable?....Pages 347-363
A Lagrangian Relaxation of the Capacitated Multi-Item Lot Sizing Problem Solved with an Interior Point Cutting Plane Algorithm....Pages 364-379
An Approximate Algorithm For A Weapon Target Assignment Stochastic Program....Pages 380-405
Continuous-based Heuristics for Graph and Tree Isomorphisms, with Application to Computer Vision....Pages 406-421
Optimization of a simplified Fleet Assignment Problem with metaheuristics: Simulated Annealing and GRASP....Pages 422-445
Towards Implementations of Successive Convex Relaxation Methods for Nonconvex Quadratic Optimization Problems....Pages 446-476
Piecewise concavity and discrete approaches to continuous minimax problems....Pages 477-488
The MCCNF Problem With a Fixed Number of Nonlinear Arc Costs: Complexity and Approximation....Pages 489-510
A New Parameterization Algorithm for the Linear Complementarity Problem....Pages 511-524
Obtaining an Approximate Solution for Quadratic Maximization Problems....Pages 525-544
Back Matter....Pages 545-560
....Pages 561-577