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.

first Moment

Required list input.

second Moment

Required list input.

beta1

Required number input.

beta2

Required number input.

learning Rate

Required number input.

epsilon

Required number input.

iteration

Required integer input.

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

First moment

The resulting first moment returned as a list.

Second moment

The resulting second moment 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.

• Adam Optimizer Step Calculator

  Calculate one scalar Adam parameter update with bias-corrected moments.

• Gradient Descent Optimizer Step

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

• L-BFGS Optimizer Step

  Compute one limited-memory BFGS two-loop direction from valid curvature-pair histories and apply a caller-supplied step size.