Optimization Definition and 588 Threads

I have a function z=f(x,y) that is reasonably well behaved (single global maximum). I can readily compute the value of z as well as partials of z with respect to x and y. I can also quite easily find the maximum. The challenge is to find the maximum and minimum values of x where c =...

Homework Statement Consider a power grid consisting of electricity producers that are connected to consumption points on the grid. The consumption points are affiliated with regional retail power companies that then distribute the power to their end users. The undirected graph (attached)...

I've just started programming with Python this summer, and I'm taking a course in computational physics this semester. I've been really enjoying it and programming in general, but I don't have much knowledge in computer science save for intro stuff (string/list methods, functions/classes...

Homework Statement Here is an alternative approach to handling absolute value terms as the decision variables: abs(x) is the smallest value z that satisfies x \leq z and -x \leq z. Using this,convert the following into a lp Min 2x1 + 3abs(x2) S.T x1 + x2 \geq 6 Homework Equations Here is a...

Here are the questions: I have posted a link there to this topic so the OP can see my work.

I'd like 2 solve the following problem (well, routinely solve a bunch of such problems): Let us have a number of points (vertices), that can be interconnected. Not any 2 points are connected. Each connection is assigned a value. I want 2 find the maximum path in the graph, that is, the one with...

Here are the questions: I have posted a link there to this topic so the OP can see my work.

I have a cost function which consists of sum of a set of quadratic loss plus a term which regularize function. my problem is: is there any way to infer probability from such a cost functions?

What exactly is "Engineering Optimization" I have the opportunity to take a grad class entitled "Engineering Design Optimization" this fall and I am curious about the subject. I have never taken an optimization class before and to be honest I don't quite understand why optimization is...

Suppose you have two poles separated by the distance $w$, the first of height $h_1$ and the second of $h_2$, where $0<h_1<h_2$. You wish to attach two wires to the ground in between the poles, one to the top of each pole, such that the angle subtended by the two wires is a maximum. What portion...

Hey Everyone, I'm having trouble setting up this word problem. I know that area of a circle is pir2 and area of a triangle is 1/2bh but for some reason I can't find a way to combine these equation together. What are the radius and area of the circle of maximum area that can be inscribed in an...

Here are the questions: I have posted a link to this topic so the OP can see my work.

Here is the question: I have posted a link there so the OP can see my work.

θHomework Statement The attached diagram depicts a sphere with several variables: the height of the cylinder, the radius of the cylinder and an angle. All that has been given to me is the hypotenuse of a triangle used. Homework Equations To my knowledge I was told to use 2sinθcosθ=sin2θ...

Hi context: The USD/CNH currency pair has been trending down at an almost linear rate past 3 years, it's safe to assume it will continue to trend downwards for the short term foreseeable future as the Chinese govt slowly allows the Yuan to appreciate to its real value. The problem: Every...

The problem is posted here: http://nrich.maths.org/5673 I tried subbing in values to get the biggest area: perimeter ratio possible. I used an arbitrary value, 12, for perimeter. For the triangle, I took out the hypotenuse and so A = 1/2(x)(y) where x+ y = 12. Its area is biggest when x = y = 6...

Homework Statement The link to the problem is here: http://i.imgur.com/wyOsoSB.png The Attempt at a Solution I'm not completely sure about my work so far so please bear with me. My professor is very poor at professing the subject so I'm trying to learn from the book. Please let me know...

Homework Statement Find the maximum point of P(h)=-10h+4410-(6800/h) Homework Equations P(h)=-10h+4410-(6800/h) The Attempt at a Solution P(h)=-10h+4410-(6800/h) P'(h)=-10+(6800/h^2) P'(0)=-10h^2+6800 10h^2=6800 Divide both sides by 10: h^2=680 and sqrt both sides: h=26.1

Here is the question: Here is a link to the question: CALCULUS needHELP WITH THIS PLEASE! APPRECIAT EIT -? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Homework Statement Joe is traveling from point A across a circular lake to a cabin on the other side at point B. The straight line distance from A to B is 3 miles and is the diameter of the lake. He travels in a canoe on a straight line from A to C. She then takes the circular trail from C to...

Homework Statement Two non-negative numbers are chosen such that their sum is 30. Find the numbers if the sum of their squares is to be a maximum. Homework Equations The Attempt at a Solution let a,b represent the two non negative numbers a=x b=30-x So, x^2+(30-x)^2=s, where...

Homework Statement Homework Equations The Attempt at a Solution I am not really sure how to optimize it from here. What should I be taking the derivative of the price function with respect to ??

1. A piece of wire 10 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How should the wire be cut so that the total area enclosed is (a) a maximum? (b) A minimum? 2. A_{s}(x) = x^{2}, A_{t}(x)=\frac{\sqrt{3}}{4}x^{2}...

Homework Statement The question is: Suppose that lim x_k=x_*, where x_* is a local minimizer of the nonlinear function f. Assume that \triangledown^2 f(x_*) is symmetric positive definite. Prove that the sequence \left \{ f(x_k)-f(x_*) \right \} converges linearly if and only if \left...

Homework Statement We want to make a conical drinking cup out of paper. It should hold exactly 100 cubic inches of water. Find the dimensions of a cup of this type that minimizes the surface area. Homework Equations SA = pi*r^2 + pi*r*l where l is the slant height of the cone. V =...

Here is the question: Here is a link to the question: Calculus Max Min problem help? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Here is the question: Here is a link to the question: I need help on a HW problem - I got the first two parts right, but am having trouble finishing the last two? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Calculate biggest and lowest value to function $$f(x,y)=x^5y^4e^{-3x-3y}$$ In the triangle has vertices in points $$\left(0,0 \right)$$,$$\left(6,0 \right)$$ and $$\left(0,6 \right)$$ Before I start I want to warn that I used google translate in the text 'In the triangle has vertices in points'...

Here is the question: Here is a link to the question: Show that the minimum and maximum points for y=f(x) occur among the min and max points for y=f^2(x).? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Here is the question: Here is a link to the question: Helpppppppppppp please !? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

I have a problem that I normally find solutions to via trial and error, and they usually aren't optimized, but was wondering if there is a better way to solve this and optimize. My application is specific but this is the best way I can describe the problem. Forgive me if it doesn't make...

Here is the question: Here is a link to the question: OPTIMIZATION PROBLEM? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Homework Statement Here is the problem, the solution and my question (in red): I'm guessing it was rejected because for the volume function, the dimensions cannot be negative? What if it was not volume and instead was just an arbitrary function. In that case you would not reject...

Here is the question: Here is a link to the question: Find the maximum and minimum values of f(x,y,z)=x^4+y^4+z^4 subject to the constraint x^2+y^2+z^2=1.? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

I'm a final year student. My final project is about power system state estimation by using particle swarm optimization (PSO). I need to create a software based on PSO. Can somebody give me some brief idea on how to start the coding and guide me about the PSO thing.

Apply Newton's method to $f(x)=(x-2)^4+(x-2)^5$ with initial guess $x_0=3$. We can observe that the sequence converges linearly with rate constant $3/4$. Now apply the iterative mathod $x_{k+1}=x_k-4f(x_k)/f'(x_k)$. This method should converge more rapidly for this problem. But how to prove that...

Homework Statement 9. This is a simplified inventory problem.Suppose that it costs c dollars to stock an item and that the item sells for s dollars. Suppose that the number of items that will be asked for by customers is a random variable with the frequency function p(k). Find a rule for...

Homework Statement A factory has stocked a lot of pipes (sufficient). Each standard pipe is 5-meter long. But this kind of pipe cannot be used directly. We should cut them into three types: 140cm, 95cm and 65cm. In addition, the proportion of these three types of pipes must be 2:4:1. In...

Perhaps forum members can advance science by solving this optimization problem from The Protein Engineer http://proteneer.com/blog/?p=1557 My statement of it: Let M be a N x N symmetric matrix such that N is divisible by 3, all the diagonal entries are 0 and each other entry is either 0...

Suppose you are given a problem to find the dimensions for the maximum volume of a cube given the surface area. These problems involve 2 equations, taking the derivative and setting it equal to zero (local minimum or maximum) and substituting the 2nd equation to find the parameters. However...

The illumination from a bulb varies directly as the intensity of the light and Intensity varies inversely as the square of the distance from the source. Two bulbs are placed 54 feet apart. The intensity, Ia, of bulb A is 64cd, and the intensity, Ib, of bulb B is 125cd. At how many feet from bulb...

I have been reading Stephen Boyd's book Convex Optimization and I have learned to form various problems like LP, QP, QCQP, SOCP or SDPs. I also learned about formulating SVM for classification problem as optimization problem. Now I am reading about Gradient Methods, Newton's method, etc...

Linear Optimization Problem follow up Maximize: z=2x2+5x2+x3 x1+x2+x3 less then or equal to 12 x1-x2 less then or equal to 15 x2+2x3 less then or equal to 10 x1, x2 and x3 is greater then or equal to 0 x1= x2= x3= s1= s2= s3= z= I get x1=2, x2=10 x3=0 s1=0 s2=0...

Homework Statement A decorative window has the form of a rectangle surmounted by a semicircle whose diameter is equal to the top of the rectangle. If the TOTAL perimeter of the window 16+pi, then what is the maximum area? A. 25.653 B. 32.148 C. 15.923 D. 38.047 E. 30.018 Correct...

Homework Statement A wholesale paint dealer is buying and distributing x cases of paint per week. She incurs the following expenses: (1) Fixed costs of $1200 (2) An expense of $60x per week representing the cost of x cases to the dealer ($60 per case) (3) A cost of $x^2/24 per week for...

Hi, I am reading Convex Optimization from Stephen Boyd's book on my own and I am stuck at math he mentions on Pg. 157 of his book which can be found here. How does he write the following: sup{uTP^{T}_{i}x | ||u||2 ≤ 1} = ||P^{T}_{i}x||2 Thanks guys

Hi, So i don't need help on any specific problem, I was just wondering if there was an easy way to solve optimization problems in calc. I have no problem doing most of it, its just that coming up with the functions is my biggest problem. Can anyone give me advice on coming up with the problems.

Homework Statement A dairy farmer plans to fence in a rectangular pasture adjacent to a river. The pasture must contain 180,000 square meters in order to provide enough gas for the herd. What dimensions would require the least amount of fencing if no fencing is needed along the river? Should...

Actually, it is really as easy as it looks. Paradoxically, it may be helpful to regard it as a special case of: 1 2 3 ...n 1 1 2 3 ...n 1 2 3 ...n 1 1 2 3 ...n 1 2 3 ...n 1 2 3 ...n 1 1 2 3 ...n 1 2 3 ...n 1 2 3 ...n 1 2 3 ...n 1 1 2 3 ...n 1 2 3 ...n 1 2 3 ...n 1 2 3 ...n 1 2 3 ...n 1...

1. A person from point A wants to get to point C diammetrically across a round lake. This person is on the shore and can walk at a rate of 4 mi/hr and row at a rate of 2 mi/hr. Which method should she use? 2. radius = 2 mi, triangle with angle θ has the points ABC 3. I started out...