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.

step Length

Required number input.

Move a specified Euclidean distance along the negative normalized gradient; this differs from learning-rate gradient descent. 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.

• Gradient Descent Optimizer Step

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

• Diagonal Trust Region Optimizer Step

  Solve a convex diagonal quadratic trust-region subproblem for a bounded Euclidean step. This is a diagonal model, not a full-Hessian solver.

• Adagrad Optimizer Step Calculator

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