LaTeX
x_{k+1}=x_k-\eta\nabla f(x_k)Variables
- x_k: current iterate
- η: step size
- ∇f: gradient
How to use this formula
Updates parameters in the direction opposite the objective gradient.
Important notes
- Step-size selection strongly affects convergence.
- Constraints require projection or another constrained method.
Quick example
For f(x)=x², the update is x_{k+1}=(1−2η)x_k.
Applicability, worked calculation, and verification
Assumptions and domain checks
- Step-size selection strongly affects convergence.
- Specify the objective, constraints, feasible domain, and any convexity or differentiability assumptions used to justify the result.
Worked example
For f(x)=x², the update is x_{k+1}=(1−2η)x_k.
Common mistakes
- Before substituting values into Gradient Descent Update, map each variable to its definition and preserve every sign, exponent, subscript, and grouping mark.
- Do not treat a stationary point as a global optimum without checking constraints, boundaries, and the required optimality conditions.
Continue the workflow
Use Gradient Descent Update in your own work
- Check the domainMatch the variables and assumptions to the problem before substituting values.
- Copy the exact notationPreserve grouping, signs, and exponents in
x_{k+1}=x_k-\eta\nabla f(x_k). - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-23
Automated quality check: Kept noindex until the missing evidence is supplied.
Formula references
- Digital Library of Mathematical FunctionsNational Institute of Standards and Technology — Definitions, notation, identities, and reference material for mathematical functions.
Frequently asked questions
What is the Gradient Descent Update used for?
Updates parameters in the direction opposite the objective gradient.
Can I copy this formula as LaTeX?
Yes. Copy x_{k+1}=x_k-\eta\nabla f(x_k) or open it in the LaTeX editor.
What should I check before using it?
Confirm that each variable, unit, domain restriction, and assumption matches the problem.