# 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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### Convex Optimization Problem with norm inequality constraint

Consider the following optimization problem: \begin{align} \inf_{x,y}&\quad(x-x_0)^\top A(x-x_0) + (y-y_0)^\top B(y-y_0) \\\text{s.t.}&\quad x^\top a\geq0,\\ & \quad y^\top b\geq0, \\& ...
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### How to find the optimal solution of a convex program given all KKT points?

Suppose we have a parametric convex program with some constraints. \begin{split} \max_{x} \: & f(x,\mathbf{a})\\ & g_1(x,\mathbf{a})\le 0 \\ & g_2(x,\mathbf{a}) \le 0 \end{...
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### Geometric interpretation of KKT conditions

I can explain why Lagrange multipliers work for scalar functions by vector calculus. Consider optimizing $f(\vec{x})$ subjected to the constraint $g(\vec{x}) = c$. At the optima, we can move ...
92 views

### KKT conditions analysis for binary constraints

I am wondering if boolean constraints in a linear program can be solved (after linear relaxation from $x\in\{0,1\}$ to both $x\ge0$ and $x\le1$) using KKT analysis. Most of the algorithms that I have ...
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### 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 ...