matlab-solve-optimization

Classify the problem first: use linprog for linear programs, quadprog for convex QPs, intlinprog for mixed-integer linear problems, lsqnonlin for nonlinear least squares, and fmincon for general constrained nonlinear problems. Always prefer the narrowest solver matching the problem structure rather than defaulting to fmincon.

Use problem-based (optimproblem, optimvar) by default for readable formulations and automatic differentiation. Fall back to solver-based when you have pre-coded objectives with exact gradients, need solver features like CheckpointFile, or require C code generation, which problem-based does not support.

Common causes are infeasible constraints, poor scaling of variables or objectives, inaccurate finite-difference gradients, or a bad initial point. Check feasibility at x0, rescale values to O(1), try the sqp algorithm, and test multiple starting points with MultiStart.

Yes, fcn2optimexpr wraps functions containing operations unsupported by automatic differentiation, such as ode45 or MEX-files, as black-boxes. The solver then uses finite differences for gradients, and you can set Analysis="off" with OutputSize to skip tracing of expensive functions.

Check the exitflag (positive means success), print output.message, and verify output.firstorderopt is below tolerance for gradient-based solvers. For problem-based solutions, use issatisfied(prob, sol) and infeasibility() to confirm constraints are satisfied.

Use surrogateopt when each function evaluation takes more than 15-20 seconds, such as simulations or MEX-based objectives. It builds a surrogate model to minimize evaluations, supports checkpointing via CheckpointFile, and returns all evaluated points in the trials output.