Use this optimization step or heuristic to study an explicitly defined objective and constraints with reproducible parameters, initialization, and stopping rules.

position

Required list input.

gradient

Required list input.

displacements

Required list input.

gradient Changes

Required list input.

learning Rate

Required number input.

Compute one limited-memory BFGS two-loop direction from valid curvature-pair histories and apply a caller-supplied step size. The tool evaluates the supplied inputs together and returns the named outputs below; it does not infer omitted operating conditions or change the units shown.^[1]

Next position

The resulting next position returned as a list.

• Convergence and solution quality depend on smoothness, convexity, scaling, gradients, conditioning, hyperparameters, randomness, constraints, and implementation details. Non-convex methods need not find a global optimum.
• Use finite inputs in the displayed units and preserve more precision than the final presentation requires. Independently verify safety-critical, financial, compliance, or production decisions.

Scale variables, monitor objective and constraint residuals, compare starts and algorithms, and verify small instances or local optimality with an independent solver.

• Nadam Optimizer Step

  Apply a bias-corrected Nesterov Adam update from caller-supplied first and second moments and the one-based iteration.

• Conjugate Gradient Optimizer Step

  Compute a Fletcher–Reeves conjugate-gradient direction and one caller-sized step from current and previous gradients.

• Gradient Descent Optimizer Step

  Apply one gradient-descent update x − η∇f; the caller supplies the gradient and learning rate.