Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fixed-Time Stable Gradient Flows: Applications to Continuous-Time
  Optimization   This paper proposes novel gradient-flow schemes that yield convergence to the
optimal point of a convex optimization problem within a \textit{fixed} time
from any given initial condition for unconstrained optimization, constrained
optimization, and min-max problems. The application of the modified gradient
flow to unconstrained optimization problems is studied under the assumption of
gradient-dominance. Then, a modified Newton's method is presented that exhibits
fixed-time convergence under some mild conditions on the objective function.
Building upon this method, a novel technique for solving convex optimization
problems with linear equality constraints that yields convergence to the
optimal point in fixed time is developed. More specifically, constrained
optimization problems formulated as min-max problems are considered, and a
novel method for computing the optimal solution in fixed-time is proposed using
the Lagrangian dual. Finally, the general min-max problem is considered, and a
modified scheme to obtain the optimal solution of saddle-point dynamics in
fixed time is developed. Numerical illustrations that compare the performance
of the proposed method against Newton's method, rescaled-gradient method, and
Nesterov's accelerated method are included to corroborate the efficacy and
applicability of the modified gradient flows in constrained and unconstrained
optimization problems.

25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph