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Strong Evaluation Complexity Bounds for Arbitrary-Order Optimization of Nonconvex Nonsmooth Composite Functions

Autor: Cartis, Coralia, Gould, Nick, Toint, Philippe L.

We introduce the concept of strong high-order approximate minimizers for nonconvex optimization problems. These apply in both standard smooth and composite non-smooth settings, and additionally allow convex or inexpensive constraints. An adaptive reg

Externí odkaz: http://arxiv.org/abs/2001.10802

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Sharp worst-case evaluation complexity bounds for arbitrary-order nonconvex optimization with inexpensive constraints

Autor: Cartis, Coralia, Gould, Nick I. M., Toint, Philippe L.

Publikováno v: SIAM Journal on Optimization, vol. 30(1), pp. 513-541, 2020

We provide sharp worst-case evaluation complexity bounds for nonconvex minimization problems with general inexpensive constraints, i.e.\ problems where the cost of evaluating/enforcing of the (possibly nonconvex or even disconnected) constraints, if

Externí odkaz: http://arxiv.org/abs/1811.01220

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Worst-case evaluation complexity and optimality of second-order methods for nonconvex smooth optimization

Autor: Cartis, Coralia, Gould, Nick I. M., Toint, Philippe L.

Publikováno v: Mathematical Programming, vol. 163(1), pp. 359-368, 2017

We establish or refute the optimality of inexact second-order methods for unconstrained nonconvex optimization from the point of view of worst-case evaluation complexity, improving and generalizing the results of Cartis, Gould and Toint (2010,2011).

Externí odkaz: http://arxiv.org/abs/1709.07180

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Evaluation complexity bounds for smooth constrained nonlinear optimisation using scaled KKT conditions, high-order models and the criticality measure $\chi$

Autor: Cartis, Coralia, Gould, Nick, Toint, Philippe L

Evaluation complexity for convexly constrained optimization is considered and it is shown first that the complexity bound of $O(\epsilon^{-3/2})$ proved by Cartis, Gould and Toint (IMAJNA 32(4) 2012, pp.1662-1695) for computing an $\epsilon$-approxim

Externí odkaz: http://arxiv.org/abs/1705.04895

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