Great question—this is one of those easy-to-overlook details in the docs if you’re not digging into the underlying logic! Let me break down exactly what happens when you omit the method parameter:

When you don’t explicitly set method, minimize() automatically selects a default based on your problem’s structure (like bounds, constraints, or variable count):

• Unconstrained problems (no bounds or constraints):
  • For problems with 1000 or fewer variables: The default is 'L-BFGS-B' (a memory-efficient quasi-Newton method ideal for medium-scale problems).
  • For problems with more than 1000 variables: It switches to 'SLSQP' (a sequential least squares programming method that handles larger scales effectively).
• Problems with bounds but no constraints:
  • The default is always 'L-BFGS-B', since this method natively supports variable bounds without extra work.
• Problems with any constraints (equality or inequality):
  • The default becomes 'SLSQP', as it’s the only built-in method that handles general constraints out of the box.

A quick edge case: For single-variable unconstrained problems, it’ll quietly use 'BFGS' instead of 'L-BFGS-B'—a simpler quasi-Newton method better suited for tiny scales.

If you want to verify this, you can look into the _select_default_method helper function in the scipy.optimize.minimize() source code—it’s where this automatic selection logic lives.

内容的提问来源于stack exchange，提问作者Chisq