English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

This paper generalizes a previously-conceived, continuation-basedoptimization technique for scalar objective functions on constraint manifoldsto cases of periodic and quasiperiodic solutions of delay-differentialequations. A Lagrange formalism is used to construct adjoint conditions thatare linear and homogenous in the unknown Lagrange multipliers. As aconsequence, it is shown how critical points on the constraint manifold can befound through several stages of continuation along a sequence of connectedone-dimensional manifolds of solutions to increasing subsets of the necessaryoptimality conditions. Due to the presence of delayed and advanced arguments inthe original and adjoint differential equations, care must be taken todetermine the degree of smoothness of the Lagrange multipliers with respect totime. Such considerations naturally lead to a formulation in terms ofmulti-segment boundary-value problems (BVPs), including the possibility thatthe number of segments may change, or that their order may permute, duringcontinuation. The methodology is illustrated using the software package coco onperiodic orbits of both linear and nonlinear delay-differential equations,keeping in mind that closed-form solutions are not typically available even inthe linear case. Finally, we demonstrate optimization on a family ofquasiperiodic invariant tori in an example unfolding of a Hopf bifurcation withdelay and parametric forcing. The quasiperiodic case is a further originalcontribution to the literature on optimization constrained by partialdifferential BVPs.

Optimization along Families of Periodic and Quasiperiodic Orbits in Dynamical Systems with Delay