# 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.

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### 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
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### Lagrange multiplier associated to an active inequality constraint

Why is the Lagrange multiplier associated to an active inequality constraint is positive. How can we see this from the KKT conditions?
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### 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 ...
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1 vote
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### Knitro dimension of lambda for Hessian

I'm trying to supply knitro with a Hessian but struggle to understand the dimension of the Lagrangian multiplier $\lambda$. From my general education and knitro's ...
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### Error while using subgradient method to update lagrange multipliers

I am trying to implemet the subgradient method in Lagragian relaxation to update the multiplier lamda which has three dimension, I have ecountered an Except error, it looks the is bugs in the code. it ...
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### constrained optimization with decreasing constraint thresholds -Literature tips

consider a constrained optimization problem (typically c=0), with f highly nonlinear: $$\text{minimize}_x f(x) \\\\ s.t \ \ \ \ g(x) \leq c$$ I experimented a bit and found ...
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### ADMM diverges on L1 regression

TLDR: Why does ADMM diverge when solving $\ell_1$ regression? Introduction I am learning about convex optimisation and wanted to solve a simple exercise that I am having issues with. I want to solve a ...
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1 vote
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### Simple nonlinear programming using convexity analysis and KKT

I want to solve the following two-variate nonlinear programming using KKT conditions:  \begin{align} \begin{split} \max \quad & 15 \sqrt{x_{1}} + 16 \sqrt{x_{2}} \\ \text{s.t.} \quad &...
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