LARGE-SCALE NONLINEAR OPTIMIZATION
Half-title
Title Page
Copyright Page
Contents
Preface
Chapter 1. Fast Linear Algebra for Multiarc Trajectory Optimization
Nicolas BΓ©rend, J. FrΓ©dΓ©ric Bonnans, Julien Laurent-Varin, Mounir Haddou, and Christophe Talbot
1 Introduction
2 Single arc problem
2.1 Framework and discretization
2.2 Linear algebra: problems without design variables
2.3 Linear algebra: problems with design variables
2.4 Mesh Refinement
2.5 Interior-point algorithms
3 Multiarc problems
3.1 Framework
3.2 Linear algebra
4 Application to Goddard's problem
5 Conclusion
References
Chapter 2. Lagrange Multipliers with Optimal Sensitivity Properties in Constrained Optimization
Dimitri P. Bertsekas
1 Introduction
2 Proof
References
Chapter 3. An O(n) Algorithm for Isotonic Regression
Oleg Burdakov, Oleg Sysoev, Anders Grimvall, and Mohamed Hussian
1 Introduction
2 Generalization of PAV algorithm
3 Complexity
4 Numerical results
5 Conclusions
6 Acknowledgements
References
Chapter 4. KNITRO: An Integrated Package for Nonlinear Optimization
Richard H. Byrd, Jorge Nocedal, and Richard A. Waltz
1 Introduction
2 Overview of the Package
3 Interior-Point Methods
3.1 Algorithm I: KNITRO-INTERIOR/DIRECT
3.2 Algorithmic Option II: KNITRO-INTERIOR/CG
3.3 Merit Function
4 Active-set Sequential Linear-Quadratic Programming
4.1 Algorithm III: KNITRO-ACTIVE
5 Projected CG Iteration
6 Special Algorithmic Features
7 Crossover
Acknowledgment
References
Chapter 5. On Implicit-Factorization Constraint Preconditioners
H. Sue Dollar, Nicholas I. M. Gould, and Andrew J. Wathen
1 Introduction
2 Constraint preconditioners
2.1 General considerations
2.2 Improved eigenvalue bounds with the reduced-space basis
3 Implicit-factorization constraint preconditioners
3.1 Structural considerations
3.2 Solution considerations
3.3 Considerations relating to preconditioning
3.4 Particular choices of P and B
3.5 Factors in other orders
4 Numerical experiments
5 Comments and conclusions
Acknowledgment
References
Chapter 6. Optimal Algorithms for Large Sparse Quadratic Programming Problems with Uniformly Bounded Spectrum
1 Introduction
2 Equality constrained problems
3 Bound constrained problems
4 Bound and equality constrained problems
5 Conclusions
References
Chapter 7. Numerical Methods for Separating Two Polyhedra
Yury G. Evtushenko, Alexander I. Golikov, and Saed Ketabchi
1 Introduction
2 Separation of polyhedra defined by inequalities
3 Separation of polyhedra defined by equations with nonnegative variables
4 The thickest separating family of parallel hyperplanes
5 The generalized Newton method
Acknowledgments
References
Chapter 8. Exact Penalty Functions for Generalized Nash Problems
Francisco Facchinei and Jong-Shi Pang
1 Introduction
2 Exact penalty functions for the GNEP
3 Updating the penalty parameters
4 Conclusions
Acknowledgments
References
Chapter 9. Parametric Sensitivity Analysis for Optimal Boundary Control of a 3D Reaction-Diffusion System
Roland Griesse and Stefan Volkwein
1 Introduction
2 The Reaction-Diffusion Optimal Boundary Control Problem
2.1 State Equation and Optimality System
2.2 Parameter Dependence
3 Properties of the Linearized Problem
4 Properties of the Nonlinear Problem
5 Numerical Results
References
Chapter 10. Projected Hessians for Preconditioning in One-Step One-Shot Design Optimization
Andreas Griewank
1 Introduction
2 (R)SQP variants on the structured KKT System
3 Pseudo-Newton Solvers and Piggy-backing
4 Necessary Convergence Condition on H*
5 Numerical Verification
6 Summary and Outlook
References
Chapter 11. Conditions and Parametric Representations of Approximate Minimal Elements of a Set through Scalarization
CΓ©sar GutiΓ©rrez, Bienvenido JimΓ©nez, and Vicente Novo
1 Introduction
2 Necessary and sufficient conditions
3 Characterizations and parametric representations
4 Conclusions
Acknowledgements
References
Chapter 12. Efficient Methods for Large-Scale Unconstrained Optimization
1 Introduction
2 Limited-memory variable metric methods
2.1 Limited memory BFGS method
2.2 Methods based on reduced Hessian matrices
2.3 Shifted variable metric methods
2.4 Shifted limited-memory variable metric methods
3 Methods for large-scale nonsmooth optimization
3.1 Principles of bundle methods
3.2 Variable metric methods for nonsmooth problems
3.3 Variable metric methods for large-scale nonsmooth problems
3.4 Variable metric methods for partially separable minimax problems
4 Hybrid methods for large-scale nonlinear least squares
5 Methods for solving large-scale trust-region subproblems
Acknowledgment
References
Chapter 13. A Variational Approach for Minimum Cost Flow Problems
Giandomenico Mastroeni
1 Introduction
2 The variational model
3 An algorithm for VI(c, K f)
4 Computational considerations and concluding remarks
References
Chapter 14. Multi-Objective Optimisation of Expensive Objective Functions with Variable Fidelity Models
Daniele Peri, Antonio Pinto, and Emilio F. Campana
1 Introduction
2 Description of the GO algorithm
3 Multi-Objective Optimisation Test
3.1 Selection of the Objective Functions
3.2 Hull Shape Modification
3.3 Active Constraints
3.4 Numerical results
4 Conclusions
Acknowledgments
References
Chapter 15. Towards the Numerical Solution of a Large Scale PDAE Constrained Optimization Problem Arising in Molten Carbonate Fuel Cell Modeling
Hans Josef Pesch, Kati Sternberg, and Kurt Chudej
1 Introduction
2 2D Molten Carbonate Fuel Cell Model
3 Simulation Results
4 Conclusions
Acknowledgement
References
Chapter 16. The NEWUOA Software for Unconstrained Optimization without Derivatives
M. J. D. Powell
1 Introduction
2 An outline of the method
3 The initial calculations
4 The updating procedures
5 The trust region subproblem
6 Subroutines BIGLAG and BIGDEN
7 Other details of NEWUOA
8 Numerical results
Appendix: Proofs for Section 3
Acknowledgements
References