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docs/src/optimization_packages/ode.md

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+# OptimizationODE.jl
+
+**OptimizationODE.jl** provides ODE-based optimization methods as a solver plugin for [SciML's Optimization.jl](https://github.com/SciML/Optimization.jl). It wraps various ODE solvers to perform gradient-based optimization using continuous-time dynamics.
+
+## Installation
+
+```julia
+using Pkg
+Pkg.add(url="OptimizationODE.jl")
+```
+
+## Usage
+
+```julia
+using OptimizationODE, Optimization, ADTypes, SciMLBase
+
+function f(x, p)
+    return sum(abs2, x)
+end
+
+function g!(g, x, p)
+    @. g = 2 * x
+end
+
+x0 = [2.0, -3.0]
+p = []
+
+f_manual = OptimizationFunction(f, SciMLBase.NoAD(); grad = g!)
+prob_manual = OptimizationProblem(f_manual, x0)
+
+opt = ODEGradientDescent(dt=0.01)
+sol = solve(prob_manual, opt; maxiters=50_000)
+
+@show sol.u
+@show sol.objective
+```
+
+## Local Gradient-Based Optimizers
+
+All provided optimizers are **gradient-based local optimizers** that solve optimization problems by integrating gradient-based ODEs to convergence:
+
+* `ODEGradientDescent(dt=...)` — performs basic gradient descent using the explicit Euler method. This is a simple and efficient method suitable for small-scale or well-conditioned problems.
+
+* `RKChebyshevDescent()` — uses the ROCK2 solver, a stabilized explicit Runge-Kutta method suitable for stiff problems. It allows larger step sizes while maintaining stability.
+
+* `RKAccelerated()` — leverages the Tsit5 method, a 5th-order Runge-Kutta solver that achieves faster convergence for smooth problems by improving integration accuracy.
+
+* `HighOrderDescent()` — applies Vern7, a high-order (7th-order) explicit Runge-Kutta method for even more accurate integration. This can be beneficial for problems requiring high precision.
+
+You can also define a custom optimizer using the generic `ODEOptimizer(solver; dt=nothing)` constructor by supplying any ODE solver supported by [OrdinaryDiffEq.jl](https://docs.sciml.ai/DiffEqDocs/stable/solvers/ode_solve/).
+
+## Interface Details
+
+All optimizers require gradient information (either via automatic differentiation or manually provided `grad!`). The optimization is performed by integrating the ODE defined by the negative gradient until a steady state is reached.
+