Function initialize_optimization_state 

pub fn initialize_optimization_state(
    problem: &mut Problem,
) -> OptimizerResult<InitializedState>

Initialize optimization state from problem and initial parameters.

This is the common initialization sequence used by all optimizers:

1. Create variables from initial values
2. Build variable-to-column index mapping
3. Build symbolic sparsity structure for Jacobian (sparse mode only)
4. Compute initial cost

The assembly mode is determined by problem.jacobian_mode.