Solve a maximization problem that is

$$\underset{{\displaystyle \frac{x}{y}}}{max}f(x/y)$$

$$\underset{{\displaystyle \frac{x}{y}}}{max}f(x/y)$$

gasavasiv
2022-10-23
Answered

Solve a maximization problem that is

$$\underset{{\displaystyle \frac{x}{y}}}{max}f(x/y)$$

$$\underset{{\displaystyle \frac{x}{y}}}{max}f(x/y)$$

You can still ask an expert for help

Miah Scott

Answered 2022-10-24
Author has **19** answers

Suppose $a$ is the point where $f$ is maximal, then, all the couples $(x,y)$ that verify $x/y=a$ are solutions to the optimization problem.

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How we can find an optimal solution for a model with concave-convex objective function?

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Let $D$ be a convex set in ${\mathbb{R}}^{n}$ and $f:D\to \mathbb{R}$ a concave and ${C}^{1}$ function. How do I show that ${x}^{\ast}$ is a global maximum for $f$ if and only if ${f}^{(1)}({x}^{\ast})y\le 0$ for all $y$ pointing into $D$ at ${x}^{\ast}$ (Here ${f}^{(1)}$ denotes the first derivative of $f$)

asked 2022-11-03

Let $f:{\mathbb{R}}^{n}\times {\mathbb{R}}^{m}\to \mathbb{R}$ be a continuous function. Suppose that there exists an ${a}_{0}\in {\mathbb{R}}^{m}$ such that $f(x,{a}_{0})$ is strictly concave in $x$. Is it true that there exists a ball $A$ around ${a}_{0}$ such that $f(x,a)$ is concave in $f(x,a)$ for $a\in A$?

asked 2022-11-18

Consider the optimization problem

$c(p)=\underset{x}{min}\sum _{i=1}^{n}{x}_{i}{p}_{i}$

subject to $f(x)\ge 1$ where $f:{\mathbb{R}}_{+}^{n}\mapsto \mathbb{R}$ is increasing and concave.

$c(p)=\underset{x}{min}\sum _{i=1}^{n}{x}_{i}{p}_{i}$

subject to $f(x)\ge 1$ where $f:{\mathbb{R}}_{+}^{n}\mapsto \mathbb{R}$ is increasing and concave.

asked 2022-10-26

Let $f$ be a concave function (and differentiable). Show that

$$\frac{f(y)-f(x)}{y-x}\ge {f}^{\prime}(y)$$

where $y>x$.

$$\frac{f(y)-f(x)}{y-x}\ge {f}^{\prime}(y)$$

where $y>x$.