Added docs for SciPy

Signed-off-by: AdityaPandeyCN <[email protected]>

Author: AdityaPandeyCN

docs/src/optimization_packages/scipy.md

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+# SciPy.jl
+
+[`SciPy`](https://scipy.org/) is a mature Python library that offers a rich family of optimization, root–finding and linear‐programming algorithms.  `OptimizationSciPy.jl` gives access to these routines through the unified `Optimization.jl` interface just like any native Julia optimizer.
+
+!!! note
+    `OptimizationSciPy.jl` relies on [`PythonCall`](https://github.com/cjdoris/PythonCall.jl).  A minimal Python distribution containing SciPy will be installed automatically on first use, so no manual Python set-up is required.
+
+## Installation: OptimizationSciPy.jl
+
+```julia
+import Pkg
+Pkg.add("OptimizationSciPy")
+```
+
+## Methods
+
+Below is a catalogue of the solver families exposed by `OptimizationSciPy.jl` together with their convenience constructors.  All of them accept the usual keyword arguments `maxiters`, `maxtime`, `abstol`, `reltol`, `callback`, `progress` in addition to any SciPy-specific options (passed verbatim via keyword arguments to `solve`).
+
+### Local Optimizer
+
+#### Derivative-Free
+
+  * `ScipyNelderMead()` – Simplex Nelder–Mead algorithm
+  * `ScipyPowell()` – Powell search along conjugate directions
+  * `ScipyCOBYLA()` – Linear approximation of constraints (supports nonlinear constraints)
+
+#### Gradient-Based
+
+  * `ScipyCG()` – Non-linear conjugate gradient
+  * `ScipyBFGS()` – Quasi-Newton BFGS
+  * `ScipyLBFGSB()` – Limited-memory BFGS with simple bounds
+  * `ScipyNewtonCG()` – Newton-conjugate gradient (requires Hessian-vector products)
+  * `ScipyTNC()` – Truncated Newton with bounds
+  * `ScipySLSQP()` – Sequential least-squares programming (supports constraints)
+  * `ScipyTrustConstr()` – Trust-region method for non-linear constraints
+
+#### Hessian–Based / Trust-Region
+
+  * `ScipyDogleg()`, `ScipyTrustNCG()`, `ScipyTrustKrylov()`, `ScipyTrustExact()` – Trust-region algorithms that optionally use or build Hessian information
+
+### Global Optimizer
+
+  * `ScipyDifferentialEvolution()` – Differential evolution (requires bounds)
+  * `ScipyBasinhopping()` – Basin-hopping with local search
+  * `ScipyDualAnnealing()` – Dual annealing simulated annealing
+  * `ScipyShgo()` – Simplicial homology global optimisation (supports constraints)
+  * `ScipyDirect()` – Deterministic `DIRECT` algorithm (requires bounds)
+  * `ScipyBrute()` – Brute-force grid search (requires bounds)
+
+### Linear & Mixed-Integer Programming
+
+  * `ScipyLinprog("highs")` – LP solvers from the HiGHS project and legacy interior-point/simplex methods
+  * `ScipyMilp()` – Mixed-integer linear programming via HiGHS branch-and-bound
+
+### Root Finding & Non-Linear Least Squares *(experimental)*
+
+Support for `ScipyRoot`, `ScipyRootScalar` and `ScipyLeastSquares` is available behind the scenes and will be documented once the APIs stabilise.
+
+## Examples
+
+### Unconstrained minimisation
+
+```@example SciPy1
+using Optimization, OptimizationSciPy
+
+rosenbrock(x, p) = (p[1] - x[1])^2 + p[2] * (x[2] - x[1]^2)^2
+x0 = zeros(2)
+p  = [1.0, 100.0]
+
+f   = OptimizationFunction(rosenbrock, Optimization.AutoZygote())
+prob = OptimizationProblem(f, x0, p)
+
+sol = solve(prob, ScipyBFGS())
+@show sol.objective   # ≈ 0 at optimum
+```
+
+### Constrained optimisation with COBYLA
+
+```@example SciPy2
+using Optimization, OptimizationSciPy
+
+# Objective
+obj(x, p) = (x[1] + x[2] - 1)^2
+
+# Single non-linear equality: x₁² + x₂² = 1
+cons(res, x, p) = (res .= [x[1]^2 + x[2]^2 - 1.0])
+
+x0   = [0.5, 0.5]
+prob = OptimizationProblem(
+    OptimizationFunction(obj; cons = cons),
+    x0, nothing, lcons = [0.0], ucons = [0.0])
+
+sol = solve(prob, ScipyCOBYLA())
+@show sol.u, sol.objective
+```
+
+### Differential evolution (global) with custom options
+
+```@example SciPy3
+using Optimization, OptimizationSciPy, Random
+Random.seed!(123)
+
+ackley(x, p) = -20exp(-0.2*sqrt(mean(x .^ 2))) - exp(mean(cos.(2π .* x))) + 20 + ℯ
+x0 = zeros(2)                    # initial guess is ignored by DE
+prob = OptimizationProblem(ackley, x0; lb = [-5.0, -5.0], ub = [5.0, 5.0])
+
+sol = solve(prob, ScipyDifferentialEvolution(); popsize = 20, mutation = (0.5, 1))
+@show sol.objective
+```
+
+## Passing solver-specific options
+
+Any keyword that `Optimization.jl` does not interpret is forwarded directly to SciPy.  Refer to the [SciPy optimisation API](https://docs.scipy.org/doc/scipy/reference/optimize.html) for the exhaustive list of options.
+
+```julia
+sol = solve(prob, ScipyTrustConstr(); verbose = 3, maxiter = 10_000)
+```
+
+## Troubleshooting
+
+The original Python result object is attached to the solution in the `original` field:
+
+```julia
+sol = solve(prob, ScipyBFGS())
+println(sol.original)  # SciPy OptimizeResult
+```
+
+If SciPy raises an error it is re-thrown as a Julia `ErrorException` carrying the Python message, so look there first.
+
+## Contributing
+
+Bug reports and feature requests are welcome in the [Optimization.jl](https://github.com/SciML/Optimization.jl) issue tracker.  Pull requests that improve either the Julia wrapper or the documentation are highly appreciated.