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- W2492704057 abstract "In this chapter we briefly consider the case of constrained nonlinear optimization problems written in the formminx∈ℝnƒ(x)s.t.x∈Ω,hi(x)≤0,i=1,…,mh,(13.1)where ƒ, hi : Ω ⊆ ℝn → ℝ ∪ {+∞} are functions defined on a set or domain Ω. We will briefly review the existing approaches for solving problems of the form (13.1) without computing or directly estimating the derivatives of the functions ƒ and hi, i = 1,…,mh, but assuming that the derivatives of the functions that algebraically define Ω are available.We emphasize the different nature of the constraints that define Ω and the constraints defined by the functions hi, i = 1,…, mh. The first type of constraints are typically simple bounds of the form l ≤ x ≤ u or linear constraints of the form Ax ≤ b. For instance, the mass of a segment of a helicopter rotor blade has to be nonnegative, or a wire used on a circuit must have a width that is bounded from below and above by manufacturability considerations. In addition, there might be linear constraints, such as a bound on the total mass of the helicopter blade.The objective function ƒ (and in some cases the constraint functions hi) is often not defined outside Ω; hence (a possible subset of) the constraints defining Ω have to be satisfied at all iterations in an algorithmic framework for which the objective function (and/or some hi's) is (are) evaluated. Such constraints are not relaxable. In contrast, relaxable constraints need only be satisfied approximately or asymptotically.If Ω is defined by linear constraints or simple bounds, then it is often easy to treat any constraints that define Ω as unrelaxable constraints. In theory Ω may also include general nonlinear constraints, whose derivatives are available. We call all the constraints that define Ω “constraints with available derivatives.” Whether to treat these constraints as relaxable or not often depends on the application and the algorithmic approach." @default.
- W2492704057 created "2016-08-23" @default.
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- W2492704057 date "2009-01-01" @default.
- W2492704057 modified "2023-10-16" @default.
- W2492704057 title "13. Review of Constrained and Other Extensions to Derivative-Free Optimization" @default.
- W2492704057 doi "https://doi.org/10.1137/1.9780898718768.ch13" @default.
- W2492704057 hasPublicationYear "2009" @default.
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