# Tagged Questions

For questions on Lagrange multipliers, a strategy to solve constrained optimisation problems.

5 views

### Optimization problem: minimize $\theta {w}^H_{{p}}{R_{nn}}{w_p} + (1-\theta){c}^T \text{diag}({p}){c}$

I have an optimization problem \label{eq:optimi_joint2} \begin{aligned} \operatorname*{minimize}_{\mathbf{w_p}\in \mathbb{C}^M,\mathbf{p}\in \{0,1\}^M} \ \ &\theta \mathbf{w}^H_{...
8 views

23 views

### Constrained optimization problem using Largange multipliers: ellipsoid collision detection and response

This one is purely for the mathematics so the result is far less important than the method itself. My task is to implement a fast and efficient ellipsoid collision detection and response algorithm. ...
36 views

### Maximizing the sum of the squares of numbers whose sum is constant

I wonder how one goes about to find the maximum of $\sum v_i^2$, the $v_i$'s being positive integers whose sum $\sum_i v_i$ is fixed.
35 views

### Minima of symmetric polynomials subject to two symmetric constraints

The homogeneous symmetric polynomial of degree $k$ in $n$ variables is $$f_k(x_1,x_2,\dots,x_n) = \sum_{i_1<i_2<\cdots<i_k}x_{i_1}x_{i_2}\cdots x_{i_k}.$$ Consider the following ...
40 views

69 views

### Find minimum and maximum on range

$f(x,y)=x^{4}-x^{2}+y^{2}$ $B={(x,y)\in \mathbb R, x^{2}+y^{2}\leq 1 }$ I should find minimum and maximum of this function on the range B. I tried it with Lagrange Multiplier and I got these points ...
53 views

24 views

### Extrema on (compact) vinculum

My textbook ask to find the extrema of $f(x,y) = 2x^2+y^2$ on $x^4-x^2+y^2-5=0$. It uses the lagrangian multipliers to find critic points.. Then it computes the function on these points then says "...
34 views

### Lagrange multipliers question with 2 constraints

Let $A=\{x\in \mathbb{R}^n|\sum x_i=n/3, \sum x_i^2=n \}$ $f(x)=\sum x_i^3$ Prove that max of f on A is of the form: $x=(a,a,.....,a,b,b...,b)$ (no need to find a or b). So with Lagrange ...
44 views

### Generalities regarding the Lagrange Multiplier

Apparently the following general statement is true. "Let $\gamma:g(x,y)=0$ be a closed curve that doesn't cross itself. If the maximisation of a function $f(x,y)$ on $g(x,y)$ using Lagrange ...
10 views

I have the following problem: $$\min_{w,\theta\ge0}\frac{1}{2}\|w-w_t\|^2+(\theta-\theta_t)^2 \text{ s.t. } w^\top(\hat n\hat z-nz)+\theta w^\top(z-\hat z)+1 \le 0,\theta-1\le 0$$ Notice that $w$ is ...
49 views

50 views

67 views

### I'm walking towards my car - when should I try the remote, in an optimal sense?

I'm interested to learn about how discrete/'event' based elements are incorporated into optimisation problems. Hopefully this is an interesting problem in its own regard, it's inspired by a daily ...