Research map / Optimization / Nonconvex and smooth optimization
Finite-Time Convergence in Continuous-Time Optimization
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add the q-rescaled gradient flow (q-RGF) with q > p for functions gradient dominated of order p in (1,q) | first-order flows (q-RGF / q-SGF) · scalar cost f(x)=|x|^p/p with p=3, c=2, x0=3/4 | finite-time convergence | Helped |
| Choose q close to p (q -> p+) in q-RGF (ablation) | q-RGF on scalar power cost · scalar cost f(x)=|x|^p/p, p=3 | settling time | Hurt |
| Use the second-order rescaled Newton flow (r=-1, alpha=1/2) with prescribed settling time | second-order flow (27) · Rosenbrock function (a=3, b=100) | convergence to minimum | Helped |
| Use Nesterov-style discretization x_{k+1}=y_k+eta F(y_k) with momentum on first-order q-RGF (ablation) | q-RGF discretization · log-sum-exp function (n=20, m=50, rho=5) | f(x_k)-f* convergence | Mixed |
| Add accelerated backtracking line search to first-order q-RGF discretization (ablation) | first-order flow discretization · log-sum-exp function (n=20, m=50, rho=5) | f(x_k)-f* convergence | Hurt |
| Add accelerated backtracking line search to second-order RNF discretization with Nesterov-style forward-Euler (ablation) | second-order flow discretization (RNF) · log-sum-exp function (n=20, m=50, rho=5) | f(x_k)-f* convergence | Helped |
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