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

Function

Required string input.

Minimum X

Required number input.

Maximum X

Required number input.

Starting points

Required integer input.

Iterations

Required integer input.

Learning rate

Required number input.

Run bounded multistart gradient descent on a selected one-dimensional non-convex benchmark. 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]

Best solution

The resulting best solution returned as an object.

• 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.

• Robust Minimax Optimization Solver

  Find a one-dimensional decision that minimizes worst squared loss across supplied scenarios.

• Stochastic Gradient Descent Step Calculator

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