Skip to main content
mistake
Source Link
Sean
  • 375
  • 1
  • 7

I have been looking at this question for a while without any progress.

Question. Maximize $$ I[\eta] = \int_0^\infty e^{-s} \Big[\cos\big(\eta(s)\big) + \cos\big(\sqrt{2}\eta(s)\big)\Big]\;ds$$$$ I[\eta] = \int_0^\infty e^{-s} \Big[\sin\big(\eta(s)\big) + \sin\big(\sqrt{2}\eta(s)\big)\Big]\;ds$$ subjected to $\eta:[0,\infty) \rightarrow \mathbb{R}$ is absolutely continuous with $\eta(0) = 0$ and $\dot{\eta}(s) \in [-1,1]$.

What are the tools (if any) available to study this kind of question (both analytically and numerically)?

I have been looking at this question for a while without any progress.

Question. Maximize $$ I[\eta] = \int_0^\infty e^{-s} \Big[\cos\big(\eta(s)\big) + \cos\big(\sqrt{2}\eta(s)\big)\Big]\;ds$$ subjected to $\eta:[0,\infty) \rightarrow \mathbb{R}$ is absolutely continuous with $\eta(0) = 0$ and $\dot{\eta}(s) \in [-1,1]$.

What are the tools (if any) available to study this kind of question (both analytically and numerically)?

I have been looking at this question for a while without any progress.

Question. Maximize $$ I[\eta] = \int_0^\infty e^{-s} \Big[\sin\big(\eta(s)\big) + \sin\big(\sqrt{2}\eta(s)\big)\Big]\;ds$$ subjected to $\eta:[0,\infty) \rightarrow \mathbb{R}$ is absolutely continuous with $\eta(0) = 0$ and $\dot{\eta}(s) \in [-1,1]$.

What are the tools (if any) available to study this kind of question (both analytically and numerically)?

Source Link
Sean
  • 375
  • 1
  • 7

Suggestions for infinite horizontal optimization

I have been looking at this question for a while without any progress.

Question. Maximize $$ I[\eta] = \int_0^\infty e^{-s} \Big[\cos\big(\eta(s)\big) + \cos\big(\sqrt{2}\eta(s)\big)\Big]\;ds$$ subjected to $\eta:[0,\infty) \rightarrow \mathbb{R}$ is absolutely continuous with $\eta(0) = 0$ and $\dot{\eta}(s) \in [-1,1]$.

What are the tools (if any) available to study this kind of question (both analytically and numerically)?