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

Scenarios

Required object input.

Minimum decision

Required number input.

Maximum decision

Required number input.

Grid step

Required number input.

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

Robust solution

The resulting robust 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.

• Non-Convex Multistart Solver

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

• Log-Barrier Interior Point Step

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

• L-BFGS Optimizer Step

  Compute one limited-memory BFGS two-loop direction from valid curvature-pair histories and apply a caller-supplied step size.