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.

barrier Weight

Required number input.

learning Rate

Required number input.

Apply one gradient step to f(x) − μ∑log(xᵢ) for strictly positive coordinates. Reject steps that leave the feasible region. 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.

• Nesterov Accelerated-Gradient Step

  Calculate one scalar Nesterov momentum update from a gradient evaluated at the lookahead point.

• Stochastic Gradient Descent Step Calculator

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