# Questions tagged [lagrange-multipliers]

For questions related to Lagrange (or Lagrangian) multipliers, coefficients used to penalize violations of constraints that have been relaxed from an optimization problem.

28 questions
Filter by
Sorted by
Tagged with
367 views

### Applicability of Lagrange Multipliers in the analysis of large-scale MILPs?

Qualitatively, in my experience in the solving of large scale MILPs, it is common that binary variables corresponding to "edge possibility" components are frequently chosen. Intuitively, these seem ...
• 550
1k views

### "Partial" Lagrangian Dual in LP

Consider the optimization problem \begin{align}\label{opt-lp}\tag{Primal} \begin{array}{cl} \underset{x \in \mathbb{R}^n}{\text{minimize}} & c^\top x \\ \text{subject to} & Ax = a \\ & Bx =...
• 3,980
121 views

### Estimate lagrangian multiplier based on instance characteristics

Assume we have a simple resource allocation problem, where all players have the same cost, but a different utility $a_s$. The resources assigned to a certain player must be between $L$ and $M$. ...
• 123
2k views

• 333
117 views

### Augmented Lagrangian Function for Semidefinite Programming Problems

I am currently reading the paper "Alternating direction augmented Lagrangian methods for semidefinite programming" and was wondering about how one comes up with the Augmented Lagrangian ...
• 33
283 views

• 233
817 views

### Why is the Lagrange Multiplier not equal the Shadow Price (Excel solver, Matlab linprog, Gurobi)?

I have a LP with equality and inequality constraints. When solving the LP with the excel-solver (GRG Nonlinear) the sensitivity report returns the lagrange multiplier for all constraints. When solving ...
• 93
139 views

### Lagrangian Multipliers for constraints in nonlinear optimization problems?

Suppose I want to optimize some function of continuous variables and the objective is nonlinear; in this context, gradient-based methods are quite popular. To my knowledge, soft constraints can be ...
• 551
227 views

### Linear Relaxation of Boolean Constraint for Solving Integer Linear Program Using KKT

I am trying to convert a boolean LP to LP using LP relaxation by converting $x \in {0,1}$ to both $x \ge 0$ and $x \le 1$. Then to use it in my problem analysis, I am trying to build the KKT ...
• 51
122 views

• 409
71 views

### Lagrange relaxation / subgaradient algorithm Sensivity to input data

I am implementing a Lagarange relaxation with subgradient method to find a lower bound for a minization problem, I tried to find the complicating constraints. I found an upper bound with relatively ...
• 1