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

Parameter

Required number input.

Gradient

Required number input.

Learning rate

Required number input.

Apply one stochastic-gradient-descent parameter update from a supplied gradient. 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]

Updated parameter

The resulting updated parameter returned as a number.

Parameter change

The resulting parameter change returned as a number.

• 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.

• Gradient Descent Optimizer Step

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

• Adagrad Optimizer Step Calculator

  Calculate one scalar Adagrad parameter update and its accumulated gradient state.

• Nadam Optimizer Step

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