Exploiting Band Structure in Unconstrained Optimization Without Derivatives
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Summary
A method combining the use of interpolation polynomials and trust-region techniques to minimize a function whose derivatives are not available and how the resulting algorithm may be adapted in a suitable way to consider problems for which the Hessian matrix is known to be sparse is discussed.
- Type
- article
- Published
- 2001-12-01
- Cited by
- 21
- References
- 37
- OpenAlex
- https://openalex.org/W75078828
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:55078863
Keywords
Hessian matrix, Computer science, Interpolation (computer graphics), Financial engineering, Mathematical optimization
References
- On the convergence of derivative-free methods for unconstrained optimization
- Trust Region Methods
- Numerical methods for unconstrained optimization and nonlinear equations
- Table errata: Algorithms for minimization without derivatives (Prentice-Hall, Englewood Cliffs, N. J., 1973)
- Recent progress in unconstrained nonlinear optimization without derivatives
- On the accelerating property of an algorithm for function minimization without calculating derivatives
- A trust-region framework for managing the use of approximation models in optimization
- A surrogate-model-based method for constrained optimization
- A Modification of Davidon's Minimization Method to Accept Difference Approximations of Derivatives
- On the Lagrange functions of quadratic models that are defined by interpolation*
- Algorithms for minimization without derivatives
- On multivariate Lagrange interpolation
- Function Minimization by Interpolation in a Data Table
- A derivative free optimization algorithm in practice
- Wedge trust region methods for derivative free optimization
- An efficient method for finding the minimum of a function of several variables without calculating derivatives
- Sequential Application of Simplex Designs in Optimisation and Evolutionary Operation
- A Method for Minimizing a Sum of Squares of Non-Linear Functions Without Calculating Derivatives
- `` Direct Search'' Solution of Numerical and Statistical Problems
- A Simplex Method for Function Minimization
Cited by
- Une méthode de région de confiance avec ensemble actif pour l'optimisation non linéaire sans dérivées avec contraintes de bornes appliquée à des problèmes aérodynamiques bruités
- Derivative Free Surrogate Optimization for Mixed-Integer Nonlinear Black Box Problems in Engineering
- Exploiting problem structure in pattern search methods for unconstrained optimization
- On convergence analysis of a derivative-free trust region algorithm for constrained optimization with separable structure
- A hybrid Hooke and Jeeves|Direct method for non-smooth optimization.
- On Curvature and Separability in Unconstrained Optimisation
- Self-Correcting Geometry in Model-Based Algorithms for Derivative-Free Unconstrained Optimization
- Optimizing partially separable functions without derivatives
- Survey of trust-region derivative free optimization methods
- Derivative-free optimization methods
- Global and local information in structured derivative free optimization with BFO
- Survey of derivative-free optimization
- Exploiting Problem Structure in Derivative Free Optimization
- The role of airspeed variability in fixed-time, fuel-optimal aircraft trajectory planning
- A Model-Based Derivative-Free Optimization Algorithm for Partially Separable Problems
- Conjunctive Bayesian Optimization (conBO): An Application to Cyber-Physical Systems Verification with Conjunctive Requirements
- Optimization Methods and Software
- A Derivative-Free Algorithm for Sparse Unconstrained Optimization Problems
- Direct Search Methods
- Trust-region algorithms for derivative-free optimization and nonlinear bilevel programming
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