# Tagged Questions

Optimization is the process of choosing the "best" value among possible values. They are often formulated as questions on the minimization/maximization of functions, with or without constraints.

22 views

55 views

### $\cos2\theta +\cos\theta +k = 0$ - set of all values of $k$ for which there is a solution

The set of all values of $k$ (real), such that the equation $\cos2\theta +\cos\theta +k = 0$ admits a solution for $\theta$ is? MY ATTEMPT: I substituted $\cos2\theta$ with $2\cos^2\theta - 1$. On ...
16 views

### Formulating a problem involving sets with ILP

Consider set $\mathcal{G} = \{G_1, \ldots, G_K\}$. We are given $\mathcal{A}_i \subset \mathcal{G}$, $i \in \mathcal{N}= \{1,\ldots, N\}$ and for each $\mathcal{A}_i$, there is a corresponding cost ...
17 views

### Recommend a optimization book with more coding examples?

I am interested in continuous optimization problems. However, I feel it is very difficult for me to understand the classic books such as Convex Optimization or Numerical Optmization. My problem with ...
35 views

### Finding a maximum with some constraints

I would like to maximize the term $l_1b_1+l_2b_2+l_3b_3-2$ such that the following conditions hold: $1>l_1>l_2>l_3>0$, $l_1,l_2,l_3 \in \mathbb{Q}$, $b_1,b_2,b_3 \in \mathbb{N}$...
31 views

### In Nonsmooth Optimization, whats the point of $x \in G$ being a local minimum results in $0 \in \delta\ f(x)+N_G(x)$

I'm reading about nonsmooth optimization and specially the book 'Nonsmooth Optimization: Analysis and Algorithms with Applications to Optimal Control' by Marko M. Mäkelä, Pekka Neittaanmäki. At page ...
42 views

12 views

### Acyclic orientation of a mixed graph with minimization of the critical path

I already asked this question as a guest but I was not able to edit it or add comments after I registered with my e-mail address. A apologize for asking the same question again. A mixed graph is a ...
23 views

27 views

### Sum/product of two functions of two variables are to be minimized

I have two functions $f(x,y)$ and $g(x,y)$ whose sum/product (whichever is possible) is to be minimized. The values of $x,y$ can vary in the interval $0<x,y<1$ (hence none of them can have a ...
21 views

### Skew-Symmetric Parts of Stochastic Matrices

It's easy to see that the set $\{W - W^T : W \in \mathbb{R}^{n \times n}\}$ is precisely the set of real skew-symmetric matrices. This continues to be the case if we restrict to (entry-wise) non-...
29 views

### Multiplying quaternions vs multiplying rotation matrices

It's a trivial question, but one I'm not 100% clear about. Given two matrices $$P_{\{1,2\}} = \left[ \begin{array}{cc}R & t \\ \textbf{0} & 1 \end{array}\right]$$ where $R$ is a 3x3 ...
68 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 ...
31 views

### Least Squares Sensitivity to data

Let ($x_1$,$y_1$),...,($x_n$,$y_n$) be my data set. I have a function $f(x,{\bf c})$ where ${\bf c}=(c_1,...,c_m)$ is a vector of $m$ parameters. I want to fit to the data using non-linear least ...
13 views

### Orient edges in a mixed graph to minimize the critical path

3 down vote favorite A mixed graph is a graph that has directed and undirected edges. Is there an efficient algorithm that allows the orientation of undirected edges in a mixed graph in such a way ...
15 views

17 views

48 views

### Why does the “printing neatly” algorithm use cubes rather than squares?

In Introduction to Algorithms, 2nd ed. (Cormen, Leiserson, Rivest, and Stein), ch. 15, Dynamic Programming, problem 15-2 Printing neatly (a copy of which is here), the official solution given in ...
21 views

### floor/ceiling/round functions in the constraints of an optimization?

I have a constrained optimization problem in which I have to impose a "floor" or "ceiling" constraint to the solution. In fact I decided to use these nonlinear rounding functions because I needed to ...
48 views

### What is the name of this problem? linear Matrix equation optimization?!

I have almost no knowledge in linear algebra but I need to understand the process of solving a problem. In fact I'm looking for some keywords or hints to know what exactly should I be Googling! So any ...
46 views

### Logistic regression for football results - Estimating coefficient through maximum likelihood

Consider two football teams $V$ and $L$ with strengths $W_V$ and $W_L$, respectively. Let's assume that the draw probability $\mathbb{P}(Draw)$ is known. Then this model is supposed to give estimates ...
### Minimize the function $f(y_1,y_2)=3 y_1^2+8y_2^2$ [closed]
I would like to minimize $f(y_1,y_2)=3 y_1^2+8y_2^2$ with the constraints $g(y_1,y_2)=y_1^2+y_2^2=1$. I thought I could use the Lagrange multipliers, but it is not work. Is there anyone could show me ...