# Questions tagged [lagrange-multiplier]

This tag is for the questions on Lagrange multipliers. The method of Lagrange multipliers (named after Joseph Louis Lagrange) provides a strategy for finding the local maxima and minima of a function subject to equality constraints.

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### variant of Levenberg-Marquardt suitable for Lagrange-Newton method

If a Newton descent is applied to some scalar function of a vector, the Hessian is positive definite in the vicinity of a minimum, but can become indefinite in larger distance from the minimum. This ...
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### Linearizing SOS1

Guys, I am trying to find ways of linearizing the operator Special Ordered Set Type 1 (SOS1). In order to understand what is my goal, I will, firstly, describe the problem I am facing. Let's consider ...
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### Alternative Proof of Lagrange Multipliers?

I think there might be a mistake in this attempted proof of Lagrange Multipliers, but I'm not sure where. Halfway through I set the total derivative of the objective function to $0$. I believe the ...
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### What is the Lagrange Multiplier value?

Is the Lagrange Multiplier typically the magnitude of the gradient of the objective function in the direction of the constraint function? Let $f(x,y,z)$ be an objective function and $g(x,y,z)=0$ be a ...
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### Comparison between surface area (wax used) of an optimized regular hexagonal prism and an optimized rhombic dodecahedron (BEE PRISM)

In my other post I was asking about the equation of volume of a rhombic dodecahedron with hexagonal base (the prism which bees use). The area is 3s(2h+(s√2)/2) and the volume is ((3s^2√3)/2)(h-s/(2√2))...
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I need a help to solve this: Find the points on the curve $x^2 + 4y^2 =4$ that are closest and furthest from the points on the curve $C: x^2 +y^2 +4x+2y=20$. My try: Let $f(x,y)=d^2(x,y)=(x-t)^2 + (y-... • 1,005 1 vote 0 answers 56 views ### Using Lagrange multiplier for finding shortest distance to implicit surface constructed by metaballs I am writing a software in which I need to find the shortest distance from an arbitrary point in 3D space to an implicit surface defined by a set of metaballs. I wanted to achieve this by using the ... 0 votes 0 answers 38 views ###$A= x^3 + y^3 +z^3 + kxyz $Let$x,y,z$are three sides of a triangle such that$x+y+z=3$. Find$k \geq 0$such that: $$A= x^3 + y^3 +z^3 + kxyz$$ have minimum. I tried for this:$k=6,k=15,k=\frac{15}{4}$and it have all ... 0 votes 1 answer 126 views ### Kuhn-Tucker conditions for inequality constraints So, when we solve the optimization problem using Lagrange Multiplier method, I know that lambda can be positive or negative. Lambda is simply the rate of change in the optimal value when the ... 0 votes 0 answers 53 views ### Lagrange multiplier method in a discretized way I succeeded in using the Lagrange multiplier method to solve continuous case, but I failed to solve discretized case. Assume$\min f(x,y) = x^2 + y^2$constraints$s.t. g(x,y) = x + y -1 = 0$use ... • 1 2 votes 0 answers 46 views ### Small changes leave the binding constraints unchanged in an optimization problem Let$X\subset \mathbb{R}^n$and$Y\subset \mathbb{R}^m$, and$f:X\times Y\to\mathbb{R}$.$f$is continuously differentiable, and for each$y\in Y$,$f(\cdot,y)$is strictly convex. Consider the ... • 1,335 1 vote 1 answer 57 views ### How should I go about solving this lagrange equation containing vectors and matrices? I have a Lagrange equation which depends on a multiplier$\lambda$. $$f(\lambda)=a^HR^{-1}a + \lambda(||a-\bar{a}||^2-\varepsilon)$$ I know$\bar{a}$,$R$and$\varepsilon$.... • 224 0 votes 0 answers 24 views ### How to determine total derivative of a multidimensional function with 2 components, when using Lagrange multipliers to determine the critical points? First of all,$g(x,y,z)= \{{(x^2+y+z),(x-3y+z^5)}\}$is the constraint given, for which the total derivate has to be determined. Btw the function given was$f(x,y,z)= x^4+y^2+z^3$which is not a ... 0 votes 0 answers 18 views ### The dual of this SDP with a simple nonconvex constraint In this problem we're optimizing over variables$X\in \text{PSD}_n$and$Y\in\mathbb R^{d\times n}$for some$d\le n. \begin{align} &\text{Maximize}&&\langle A_0, Z\rangle\\ &\... • 66 1 vote 1 answer 69 views ### Find\max_{ x,y \in [b,1],\frac{p}{x} + \frac{1-p}{y} =a, p \in [0,1]} \left( p x^2 +(1-p) y^2 \right)\$

I am struggling to solve the following optimization problem: \begin{align} \max_{ x,y \in [b,1],\frac{p}{x} + \frac{1-p}{y} =a, p \in [0,1]} \left( p x^2 +(1-p) y^2 \right) \end{align} where we ...
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