Overview
ADMM splits an objective into easier subproblems, coordinates them with an augmented Lagrangian, and updates a dual variable to enforce agreement.
SpecializedSource checked
ADMM
Solves constrained optimization problems by alternating primal updates and dual correction.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Optimization
- Difficulty
- Advanced
- Family
- Constrained Optimization
- Tier
- Specialized
- Status
- Verified
- Review
- Source Checked
- Sources
- 1
- Formulas
- 1
- Relationships
- 2
- Code example
- Ready
- Visualization
- Ready
- Aliases
- Alternating Direction Method of Multipliers
Core Concepts
augmented lagrangianvariable splittingdual updateconstraint residual
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(step cost)
Average
O(iterations * step cost)
Worst
O(iterations * step cost)
Space
O(problem state)
When to Use
- Use when tuning model parameters needs augmented lagrangian.
- Use when the input matches the assumptions behind constrained Optimization.
When Not to Use
- Avoid when the objective is cheap and convex enough for a simpler exact solver.
- Avoid when a simpler algorithm gives the required result with less setup.
What It Does
- Solves constrained optimization problems by alternating primal updates and dual correction
- Uses augmented lagrangian and variable splitting to guide the work.
- Produces best candidate.
Use Cases
- Tuning model parameters
- Searching design spaces
- Fitting models to noisy data
Inputs
- Objective function
- Initial candidate or population
- Stopping rule
Outputs
- Best candidate
- Objective value
- Search history
Key Formulas (1)
Dual update
unext = u + A·x + B·z − c
u_next = u + A*x + B*z - cAccumulates constraint violation after primal subproblem updates.
Pseudocode
- 1.Prepare the inputs and state needed for ADMM.
- 2.Apply the augmented lagrangian step while the stopping condition has not been met.
- 3.Update intermediate state and discard invalid candidates.
- 4.Return best candidate.
Canonical Example
- Input
- ADMM input with a small representative case
- Output
- Best candidate
- Explanation
- ADMM applies augmented lagrangian to produce best candidate.
Implementation Notes
- Track both best-so-far and current candidate state.
- Keep the augmented lagrangian step separate enough to test independently.
Common Pitfalls
- Stopping too early can make a poor local result look like convergence.
- Forgetting to check edge cases can make ADMM look correct on only ideal inputs.
Interactive Mechanism Walkthrough
Iterative Convergence & State TrajectoryPlot candidate points, objective values, and improvement steps across iterations.
Step 1 of 4: Prepare the inputs and state needed for ADMM.
optimization-mechanismNotes
ADMM is most reliable when the splitting matches the problem structure and residual tolerances are monitored.
Sources (1)
What each reference supports for this entry.
Boyd ADMM paper
PaperFoundations and Trends reference for ADMM in distributed optimization and statistical learning.
Open sourceExplore Next
Good next jumps from the relationship graph, ranked for useful discovery.
Relationships
View full relationship pageConceptual neighborProximal Gradient Method
Both use proximal-style updates for structured optimization problems.
Tags
OptimizationConstraint SolvingAlternating DirectionConvex Optimization