Large-Scale Nonlinear OptimizationGianni Pillo, Massimo Roma Large-Scale Nonlinear Optimization reviews and discusses recent advances in the development of methods and algorithms for nonlinear optimization and its applications, focusing on the large-dimensional case, the current forefront of much research. The chapters of the book, authored by some of the most active and well-known researchers in nonlinear optimization, give an updated overview of the field from different and complementary standpoints, including theoretical analysis, algorithmic development, implementation issues and applications. |
Contents
| 15 | |
An Integrated Package for Nonlinear Optimization | 35 |
On implicitfactorization constraint preconditioners | 60 |
Optimal algorithms for large sparse quadratic programming | 83 |
Exact penalty functions for generalized Nash problems | 114 |
Projected Hessians for Preconditioning in OneStep OneShot | 151 |
Conditions and parametric representations of approximate | 172 |
A variational approach for minimum cost flow problems | 211 |
Towards the Numerical Solution of a Large Scale PDAE | 242 |
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adjoint algorithm analysis applied approximate solutions assumption b₁ b₂ BFGS method components compute constrained optimization convergence convex defined denote derivative design variables differentiable efficient eigenvalues equality constraints equation factorization feasible formula given global GNEP GPAV Hessian matrix implemented initial interior-point interpolation points isotonic regression iteration Jacobian KNITRO Lagrange multipliers Lagrangian line search linear Mathematical matrix minimization monotone NEWUOA nonlinear optimization nonlinear programming nonsmooth norm objective function obtained optimal control optimal control problem optimal solution optimisation optimization problem Pareto Pbeg penalty parameter polyhedra positive definite preconditioners preconditioning quadratic model quadratic programming satisfies scalar Section separating hyperplanes SIAM Journal solving sparse step subproblem Theorem tion trust region unconstrained updating variable metric methods variational inequality vector X₁ X1 and X2 zero