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.

hessian Diagonal

Required list input.

radius

Required number input.

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

Step

The resulting step 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.

• Steepest Descent Optimizer Step

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

• BFGS Optimizer Step Calculator

  Calculate a scalar BFGS inverse-Hessian update and the next parameter step.

• Newton Optimizer Step Calculator

  Calculate one damped scalar Newton optimization step from a gradient and Hessian.