WIP [Optapp] Restart Optimization Process

[Igarizza]

📝 Description

Adds restart capability to the OptimizationApplication: an optimization run can now checkpoint its full in-memory state (problem data, controls, algorithm, convergence-criteria bookkeeping) to disk and resume from it later, continuing at the same step with the same internal state instead of re-initializing from scratch.

Tags: OptimizationApplication, SystemIdentificationApplication

Key changes

New OptimizationProblemRestartOutputProcess / OptimizationProblemRestartInputProcess to checkpoint and reload the OptimizationProblem's state (pickled BufferedDict tree, tensors converted to numpy since TensorAdaptors aren't picklable).
OptimizationProblem.SetStep() to let the restart process set the step counter without cycling the buffer.
Several algorithms/controls/convergence-criteria made restart-safe by persisting cross-iteration state into unbuffered data.
optimization_analysis.py: execution policies now initialize before processes.
A small, seemingly unrelated change in SystemIdentificationApplication/measurement_residual_response_function.cpp (dropped const, added commented-out debug code) — flagged for you to confirm before merge.
Validation

New test_steepest_descent_restart.py: runs to a step, restarts, and checks the resumed run matches an uninterrupted run.
Full text is at /tmp/claude-1000/-home-ihar-Software-Kratos-optapp/b2f4ea9d-756d-4a5f-bfa4-dc6a50995edc/scratchpad/pr_description.md.

[Copilot]

Pull request overview

Adds restart/checkpoint capability to the OptimizationApplication so an optimization run can persist its full in-memory state to disk and later resume without re-initializing algorithm/control/convergence bookkeeping.

Changes:

• Introduces restart input/output processes that snapshot/restore OptimizationProblem state (including buffered data and tensor fields).
• Makes several controls, projections, and convergence criteria restart-safe by persisting cross-iteration state in unbuffered data.
• Adds a steepest-descent restart regression test and adjusts initialization ordering in optimization_analysis.py.

Reviewed changes

Copilot reviewed 17 out of 18 changed files in this pull request and generated 6 comments.

Show a summary per file

File	Description
applications/SystemIdentificationApplication/custom_responses/measurement_residual_response_function.cpp	Minor formatting/line-ending adjustment.
applications/OptimizationApplication/tests/test_OptimizationApplication.py	Registers the new restart test in the suite.
applications/OptimizationApplication/tests/algorithm_tests/analysis_based_tests/algorithm_steepest_descent_restart/test_steepest_descent_restart.py	New end-to-end test validating restart equivalence.
applications/OptimizationApplication/tests/algorithm_tests/analysis_based_tests/algorithm_steepest_descent_restart/optimization_parameters.json	New parameters file for the restart test case.
applications/OptimizationApplication/python_scripts/utilities/optimization_problem.py	Adds SetStep() to support restore without cycling buffers.
applications/OptimizationApplication/python_scripts/utilities/opt_projection.py	Extends projections to accept/store restart data for adaptive state.
applications/OptimizationApplication/python_scripts/processes/optimization_problem_vtu_output_process.py	Changes VTU output behavior for sub model parts.
applications/OptimizationApplication/python_scripts/processes/optimization_problem_restart_output_process.py	New checkpoint writer process for restart payloads.
applications/OptimizationApplication/python_scripts/processes/optimization_problem_restart_input_process.py	New checkpoint reader process to restore problem state.
applications/OptimizationApplication/python_scripts/optimization_analysis.py	Moves execution-policy initialization earlier (before processes).
applications/OptimizationApplication/python_scripts/convergence_criteria/patience_conv_criterion.py	Persists/re-hydrates evolving state via unbuffered data.
applications/OptimizationApplication/python_scripts/convergence_criteria/max_iter_conv_criterion.py	Adjusts validation logic for max_iter.
applications/OptimizationApplication/python_scripts/convergence_criteria/magnitude_reduction_conv_criterion.py	Re-hydrates target value on restart.
applications/OptimizationApplication/python_scripts/convergence_criteria/l2_conv_criterion.py	Forces scalar float type for stored norm.
applications/OptimizationApplication/python_scripts/convergence_criteria/avg_abs_improvement_conv_criterion.py	Persists/re-hydrates evolving state via unbuffered data.
applications/OptimizationApplication/python_scripts/controls/thickness/shell_thickness_control.py	Wires projection restart data into thickness control.
applications/OptimizationApplication/python_scripts/controls/material/simp_control.py	Wires projection restart data into SIMP control projections.
applications/OptimizationApplication/python_scripts/algorithms/standardized_rgp_constraint.py	Persists evolving coefficients in unbuffered data for restart.

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