2
votes
0answers
53 views

Maximize a function subject to the constraint $x^2+y^2=R^2$

Please help me how to deal with maximization of function $$f(x,y)=1-e^{-\pi x}+e^{\pi x}\left[1-\cos(\pi y)+\sin(\pi y)\right]$$ subject to the constraint $x^2+y^2=R^2$. Using Lagrange ...
0
votes
0answers
39 views

How do I find out if a critical point of a function is a maximum or a minimum?

If I've found the critical point of a function defined in some constraint (perhaps using Lagrange multipliers and the like); how do I find out if it's a relative/global maximum/minimum of a function ...
0
votes
1answer
34 views

Uniqueness of Solution to non linear polynomial equations given by lagranges method

When considering Lagrange's method of multipliers for finding maximal solutions to a set of non-linear equations, I have reached a set of 4 equations in 4 real unknowns, $(a,b,c,\lambda)$: ...
1
vote
1answer
49 views

Help to understand the setting up of this Lagrangian

So..I understand up to step 4..but then there are these things I dont get, to start with , it says on (5) that the utility function depended only on the ratios p1/w p2/w ?? why does it say that? ...
1
vote
0answers
65 views

Methods to minimise multilinear functions with trilinear, quad-linear and higher-linear terms?

My goal is to minimize functions such as $$f_1(\mathbf{p})=p_1p_3p_7+p_1p_4p_7+p_2p_3p_7+p_2p_4p_7-p_1p_3p_5p_6-p_1p_4p_5p_6-p_2p_3p_5p_6-p_2p_4p_5p_6$$ and ...
2
votes
2answers
335 views

How can I solve Lagrange multiplier equation with multi constraints?

This site is really awesome. :) I hope that we can share our ideas through this site! I have an equation as below, $$ min \ \ w^HRw \ \ subject \ \ to \ \ w^HR_aw=J_a, \ w^HR_bw=J_b$$ If there is ...
3
votes
1answer
320 views

Lagrange Multipliers for Function Spaces

For some constant $A > 1$ I am trying to solve the constrained minimization problem minimize $F(u)$ in $C$ subject to $H(u) = 0$. Here $F(u) = \int -u dx$ and $H(u) = \int \sqrt{1 + (u')^2} dx - ...
1
vote
1answer
471 views

Constrained Optimization - Lagrange Multipliers (Example)

Let $f(x, y, z) = xyz$ $h1(x, y, z) = x + y + z − 4$5 and $h2(x, y, z) = 2x − y$. Goal: Minimize $f(x, y, z)$ subject to $h1(x, y, z) = 0$ and $h2(x, y, z) = 0$. First part: Show that every ...
1
vote
1answer
142 views

Lagrange method - non-linear system of equations

I have to compute optimal parametres of truncated cone so that its Volume is fixed (lets say it is 1) and its surface is minimal using Lagrange method These are equations desribing my object: ...