Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [optimization]

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.

In mathematics, computer science, economics, or management science, mathematical optimization (alternatively, optimization or mathematical programming) is the selection of a best element (with regard to some criteria) from some set of available alternatives.

An optimization problem can be represented in the following way: given a function $f:A\to\mathbb{R}$ from some set $A$ to the real numbers, we want to find an element $x_0\in A$ such that $f(x_0)\le f(x)$ for all $x \in A$ ("minimization") or such that $f(x_0)\ge f(x)$ for all $x \in A$ ("maximization").

22512 questions
0
votes
0 answers

KKT conditions for non-convex almost everywhere differentiable problems

Consider the context of constrained function minimization. The well-known KKT conditions do not require the objective or constraint functions to be convex, but they do require them to be differentiable. On the other hand, if the problem is convex,…
Manos
  • 25,833
0
votes
3 answers

What is the closest point on the graph of $x^2-y^2=4$ to the point $(0,1)$?

If there is a point (a,b) on the hyperbola $x^2-y^2=4$ that is closest to the point (0,1), then what is this point? I prefer this problem to be solved with the knowledge of the the maximum and minimum using the derivatives and so on. I am a bit…
Maher
  • 607
0
votes
0 answers

How do you find the minimum distance between two skew planes?

I know how to find the minimum distance between 2 skew lines. Does that help me with skew planes?
Aubrey
  • 21
0
votes
1 answer

optimization with non smooth constraint

I am trying to maximize the profit of a power plant. I have a constraint which is that the power plant, when operating, has a minimum and maximum capacity. (So a power block either has an output of zero or between min-max capacity). I am considering…
Jesse RJ
  • 45
0
votes
1 answer

a calculus optimization problem

Given points A(2,1) and B(5,4), find the point on the x-axis P(x,0) in the interval [2,5] that maximizes the angle APB. How can I devise an optimize equation and a constraint equation out of this?
user194325
  • 1
0
votes
1 answer

convert summation to matrix formula: why is it true

Assume we have a matrix $Y \in R^{n \times k}$ and a matrix $W \in R^{n \times n}$ that gives mutual weight between each $n$ datapoints $y_i$ and $y_j$. Also we define degree matrix $D_{ii} = \sum_{j=1}^n W_{ij}$ as a diagonal matrix. Why minimizing…
Learner
  • 3
0
votes
1 answer

Optimization problem with open box to be constructed

An open box is to be constructed so that the length of the base is $3$ times larger than the width of the base. If the cost to construct the base is $5$ dollars per square foot and the cost to construct the four sides is $4$ dollars per square foot,…
Ozi
  • 17
0
votes
1 answer

Steepest descent method analytically

I want to use steepest descent method to minimize the function below and show the first method of iteration analytically with starting point xt[1,1] f(x) = x^3 + xy + x^2y^2 – 3x I have gone to the point where I know the next point x1 is found by…
Amaa
  • 5
0
votes
1 answer

Solving for critical points

I calculated cost to find a minimum as $C=0.11xy+0.12xz+0.12yz$ for volume $xyz=668.25$. I ended up with critical points $c_x=0.11-80.19y^2=0$, and $c_y=0.11y-80.19x^2=0$ after makin the function $2$ variable by solving for z and substituting into…
Phelvrey
  • 11
0
votes
1 answer

Two-constraints optimization?

How would one go about trying to calculate the highest/lowest values of a two variable function given that $(x,y)$ must lie on the upper half of the unit circle? If it was just the unit circle, I'd set the partiel derivatives of $f$ equal to the…
Jackson Dan
  • 51
-1
votes
1 answer

How do I set up the following problem to arrive at the answer?

A warehouse has 10 unlabelled rows of pallets. Each row of pallets contains thousands of cell phones destined for different countries. Each 100 gram cell phone is exactly the same except for those in the row destined for Japan, which have a…
Dennis
-1
votes
2 answers

finding minimum and maximum distances using Lagrange's method

I could not solve the following problem, please help me Suppose that a satellite is rotating in an elliptical orbit keeping the earth at the center point. Show using Lagrange theory, that the maximum and minimum distances of the satellite from the…
avi
  • 1
-1
votes
2 answers

Absolute maximum and absolute minimum of f(x)= ln x on [1,2]?

Can somebody help me with this one. Find the absolute maximum and absolute minimum of $f(x)$ = $ln(x)$ on $[1,2]$.
ath13
  • 1
-1
votes
1 answer

optimize travel time on a 2d plane

There is a dog at (x,y) = (37,10) with units say feet. The dog wants to go home located at origin (0,0). The dog speed is 6 feet/seconds on the x,y axes and 6.5 anywhere else. What's the fastest path to the origin? My answer says a direct path but…
user147813
  • 13
-1
votes
2 answers

distance between two points $A$ and $B$, one point is set parametrically

$A$ is a point set parametrically with $x = 2u+4v$, $y = 2u+2v$, $z = 3u+4v$. Point $B$ is given by $(-5, -1, -3)$. I need to find the smallest distance between points $A$ and $B$.
Денис Денис
  • 27
1 2 3
…
97 98