Improve documentation for solve function results

Addresses issue #587 by adding comprehensive documentation about the OptimizationSolution object returned by solve(), including:
- Detailed explanation of all solution fields (u/minimizer, objective/minimum, retcode, stats, etc.)
- Clear documentation about the aliases (u/minimizer and objective/minimum)
- Example code showing how to access and use solution information
- Array interface documentation
- Cross-references between related documentation pages

This helps users understand what properties are available in the solution object and how to use them effectively.

🤖 Generated with [Claude Code](https://claude.ai/code)

Co-Authored-By: Claude <[email protected]>

Author: ChrisRackauckas

docs/src/API/optimization_solution.md

@@ -3,3 +3,24 @@
 ```@docs
 SciMLBase.OptimizationSolution
 ```
+
+## Accessing Solution Information
+
+The `OptimizationSolution` type is returned by the `solve` function and contains all information about the optimization result. Here's a quick reference for the most commonly used fields:
+
+### Solution Values
+- `sol.u` or `sol.minimizer`: The optimal parameter values
+- `sol.objective` or `sol.minimum`: The objective function value at the optimum
+
+### Convergence Information
+- `sol.retcode`: Return code indicating termination reason
+- `sol.stats`: Detailed statistics about the optimization process
+
+### Aliases
+For user convenience, the following aliases are provided:
+- `sol.minimizer` is an alias for `sol.u`
+- `sol.minimum` is an alias for `sol.objective`
+
+These aliases allow you to use terminology that feels more natural for your specific problem context.
+
+For detailed examples and usage patterns, see the [Common Solver Options](@ref) section.

docs/src/API/solve.md

@@ -3,3 +3,65 @@
 ```@docs
 solve(::OptimizationProblem,::Any)
 ```
+
+## Understanding the Solution Object
+
+The `solve` function returns an `OptimizationSolution` object that contains the results of the optimization. This object has several important fields that provide information about the solution and the optimization process.
+
+### Main Solution Fields
+
+- **`sol.u`** or **`sol.minimizer`**: The optimal values found by the optimizer. These are aliases - both refer to the same solution vector. Use whichever feels more natural for your problem context.
+  
+- **`sol.objective`** or **`sol.minimum`**: The objective function value at the solution point. These are also aliases for the same value.
+
+- **`sol.retcode`**: The return code indicating how the optimization terminated. Common values include:
+  - `ReturnCode.Success`: Optimization converged successfully
+  - `ReturnCode.MaxIters`: Maximum iterations reached
+  - `ReturnCode.MaxTime`: Maximum time limit reached
+  - `ReturnCode.Failure`: Optimization failed (check solver output for details)
+
+- **`sol.stats`**: Statistics about the optimization process, including:
+  - `iterations`: Number of iterations performed
+  - `time`: Total computation time
+  - `fevals`: Number of objective function evaluations
+  - `gevals`: Number of gradient evaluations (if applicable)
+
+- **`sol.original`**: The original output from the underlying solver package (solver-specific)
+
+- **`sol.cache`**: The optimization cache used during solving (advanced use)
+
+### Example Usage
+
+```julia
+using Optimization, OptimizationOptimJL
+
+# Define and solve an optimization problem
+rosenbrock(u, p) = (p[1] - u[1])^2 + p[2] * (u[2] - u[1]^2)^2
+optf = OptimizationFunction(rosenbrock, Optimization.AutoForwardDiff())
+prob = OptimizationProblem(optf, zeros(2), [1.0, 100.0])
+sol = solve(prob, Optim.BFGS())
+
+# Access solution information
+println("Solution: ", sol.u)  # or sol.minimizer
+println("Objective value: ", sol.objective)  # or sol.minimum
+println("Return code: ", sol.retcode)
+println("Iterations: ", sol.stats.iterations)
+println("Function evaluations: ", sol.stats.fevals)
+println("Total time: ", sol.stats.time, " seconds")
+
+# Check if optimization was successful
+if sol.retcode == ReturnCode.Success
+    println("Optimization converged successfully!")
+end
+```
+
+### Array Interface
+
+The solution object also supports an array interface for convenience:
+
+```julia
+# Access solution components like an array
+sol[1]  # First component of the solution vector
+sol[:]  # All components (same as sol.u)
+length(sol)  # Number of optimization variables
+```