# 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.

34 views

### Linear programming optimization problem

I need some hint, where I can find programming algorithm for next optimization problem. I need to write a code to solve some system of equations with several restrictions. Let's assume, we have $N$ ...
9 views

### Prove that, if $x^*$ is such that $Ax^*=c$, $x^*\geq 0$, then $x^*$ is a optimal solution.

Let $A\in\mathbb{R}^{n\times n}$ a symetric matrix. Consider the lineal problem $$\min{c^Tx}$$ s.t. $Ax\geq c$, $x\geq 0$. Prove that, if $x^*$ is such that $Ax^*=c$, $x^*\geq 0$, then $x^*$ is a ...
26 views

### MILP how to make constraints numbers as a decision variable

I am trying to build a MILP. I need to set the number of linear constraints in the model as a decision variable. For example: ...
49 views

### Calculate lesser value that can take the side c=? [on hold]

EDIT: Consider a right triangle , it is satisfied that: $ab + bc + ac = 100$ Determine the smallest value that the side $c$ can take (without brute force)
14 views

### Is the CMF of a log-concave PMF also log-concave?

If a PDF is log-concave, then its CDF is also log-concave. The proof I know for this uses the derivative of the log function, see Proposition 1 in this paper. Does this also hold for discrete ...
459 views

### Relationship between maximum and minimum of a function

Does $\max(f) = -\min(-f)$ hold generally?
52 views

### Optimal Apple Eating Strategy

You hate apples. As a result, you have angered the apple king and are being punished. You will have to eat $n$ apples before the apple king is willing to let you leave. The apples are marked from $1$ ...
64 views

### Literature study for Optimal Estimation Theory

It seems Optimal Estimation/Control Theory requires a lot more than undergraduate maths. Any good book that would help me get started? I have so far referred the following books but found them quite ...
106 views

### What is the optimal route for visiting Pokéstops in Pokémon Go?

Okay, I've got a fun problem for you, which was not suited for the gaming stackexchange: Pokéstops are GPS locations with a certain radius. When you are in the radius, you can get certain ingame ...
10 views

28 views

### Equivalence between standard optimization problem and Langragian form

Given a problem: $$\min_x f(x)$$ subject to $$g(x) \le C$$ In general, when it is equivalent to the problem $$\min_x f(x) + \lambda g(x)$$ for certain $\lambda$? Here my equivalence means : the ...
21 views

21 views

### Solving simple LP problem with Lagrange multipliers

Hi just as a test I'm trying to solve the following LP with Lagrange multipliers. $min -x_1$ $s.t$ $x_2 \leq 1 - x_1$ $x_1, x_2 \geq 0$ I add slack variables to have a equality constrained LP ...
5 views

### Optimisation: mayer, lagrange and bolza problem

Regarding the determination of an optimal curve, can someone please help me and define the mentioned problems in words, i.e. when to use what. I know, that a bolza problem is the combination of mayer ...
31 views

### Confusion of a formula about Lagrangian

Recently, I am reading a paper about eigenvalue problems. Consider the following problem, which occurs at the first page of the paper. \begin{align} \text{minimize}\quad &x^TAx \\ \text{subject ...
50 views

### Meaning of $Ax \leq b$

I continue to come across $Ax \leq b$ or $Ax= b$ in optimization problem, but I am having trouble interpreting the meaning of this. Does this have a similar meaning to the following (Cramer's Rule) ...
20 views

### From constrained to unconstrained optimization

I have the following convex optimization problem: \label{prob} \begin{aligned} &\underset{{\bf W, \xi}}{\text{min}} & \frac{1}{2} ||{\bf W}||_2^2 + \sum_{i=1}^n C_{y_i}\max(0,...
32 views

### Existence of absolute maxima and minima

In which of the following functions can be guaranteed the existence of absolute maxima and minima? a) $f(x,y,z)=x+y$ with $z\geq x^2+y^2+1$. b) $f(x,y)=\ln (x^2+y^2+1)$, with $x\geq 0$ and $y\geq 0$...
30 views

### What is the coordinate of the maximum value of a quadratic function given by two points and axis?

There are only three pieces of information available: the graph passes through (0,0) and (6,0) the symmetry axis is $x$ = 3 the graph is downward My attempt: I've tried to work on ...
The actual problem reads: Find the area of the largest rectangle that can be inscribed in the ellipse $$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1.$$ I got as far as coming up with the equation ...