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Finance Notes_Part_4 - 3 Optimization under general...

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Classes of algorithms (globally convergent) Line-Search Methods : Aim to get descent along negative simplex gradients (which are intimately related to polynomial models). Examples are the implicit filtering method. Audet and Vicente (SIOPT 2008) Introduction 18/109
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Classes of algorithms (globally convergent) Trust-Region Methods : Minimize trust-region subproblems defined by fully-linear or fully-quadratic models (typically built from interpolation or regression). Examples are methods based on polynomial models or radial basis functions models. Audet and Vicente (SIOPT 2008) Introduction 19/109
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Presentation outline 1 Introduction 2 Unconstrained optimization Directional direct search methods Simplicial direct search and line-search methods Interpolation-based trust-region methods
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Unformatted text preview: 3 Optimization under general constraints 4 Surrogates, global DFO, software, and references Direct search methods Use the function values directly. Do not require derivatives. Do not attempt to estimate derivatives. Mads is guaranteed to produce solutions that satisfy hierarchical optimality conditions depending on local smoothness of the functions. Examples: DiRect , Mads , Nelder-Mead, Pattern Search. Audet and Vicente (SIOPT 2008) Unconstrained optimization 21/109 Coordinate search (ancestor of pattern search). Consider the unconstrained problem min x ∈ R n f ( x ) where f : R n → R ∪ {∞} . Audet and Vicente (SIOPT 2008) Unconstrained optimization 22/109...
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