Problem 4. Let f : R –→ R be a twice differentiable function. Consider the first order differential equation dx(t) df (x(t)) = k dt dx a)Derive conditions on the parameter k and the second derivative of f, so that the local minima of f(x) are asymptotically stable. b) Explain how this ordinary differential equation can be used to construct a optimization algorithm in order to find the minima of function f if the minima are not a priori know analytically. Can we always guarantee that we can find the global minima of the function f(x)? Explain why or why not.
Problem 4. Let f : R –→ R be a twice differentiable function. Consider the first order differential equation dx(t) df (x(t)) = k dt dx a)Derive conditions on the parameter k and the second derivative of f, so that the local minima of f(x) are asymptotically stable. b) Explain how this ordinary differential equation can be used to construct a optimization algorithm in order to find the minima of function f if the minima are not a priori know analytically. Can we always guarantee that we can find the global minima of the function f(x)? Explain why or why not.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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