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Unconstrained Optimization Techniques
2021The numerical algorithms to be developed for optimal control computation in this book are based on the control parametrization technique in conjunction with a novel time scaling transform. Essentially, an optimal control problem with its control functions being approximated by an appropriate linear combination of spline functions is reduced to an ...
Kok Lay Teo +3 more
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1996
Abstract As can be seen, the higher-order derivatives of a quadratic function are all zero. From a Taylor expansion (the first three terms are always exact) it follows that all functions with continuous second derivatives behave much the same as quadratic functions provided the region is small enough.
P Neittaanmäki, M Rudnicki, A Savini
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Abstract As can be seen, the higher-order derivatives of a quadratic function are all zero. From a Taylor expansion (the first three terms are always exact) it follows that all functions with continuous second derivatives behave much the same as quadratic functions provided the region is small enough.
P Neittaanmäki, M Rudnicki, A Savini
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Unconstrained Optimization Problems
2010Unconstrained optimization methods seek a local minimum (or a local maximum) in the absence of restrictions, that is, $$f(x) \longrightarrow \min (x \in D)$$ for a real-valued function f: D → ℝ defined on a nonempty subset D of ℝ n for a given n ∈ ℕ.
Wilhelm Forst, Dieter Hoffmann
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Unconstrained Optimization Algorithms
2019In this chapter, we will present the most representative algorithms for solving an optimization problem without functional constraints, that is, the problem $$ \begin{array}{lll} P: &{} \text {Min} &{} f(x) \\ &{} \text {s.t.} &{} x\in C, \end{array} $$ where \(\emptyset \ne C\subset \mathop {\mathrm {dom}}f\subset \mathbb {R}^{n}.\) We will ...
Francisco J. Aragón +3 more
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Large-Scale Unconstrained Optimization
This work is a survey on the methods for large scale unconstrained optimization. Besides its own theoretical importance, the growing interest in the last years in solving problems with a larger and larger number of variables are arising very frequently from real world as a result of modeling systems with a very complex structure. In this paper the mainopenaire +2 more sources