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Are there any algorithms for finding the maximum value of a continuous function, which is proofed to be bounded upside?
For example, a function similar to sin.
I think Newton's method and Mid-point method are for finding a fixed value, any other methods for finding maximum value?
For general functions that are "Lipschitz-continuous" (meaning that the output changes by at most a constant factor times the change in input) see e.g. http://link.springer.com/article/10.1007%2FBF00938542#page-1 and http://link.springer.com/article/10.1007%2Fs10898-012-9937-9#page-1 . If your function is arbitrary continuous and not Lipschitz-continuous, then in theory the function could change to an arbitrarily high or low value over an arbitrarily small region, so provable global optimization is very hard.
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I need to do a job where I need to place a particular object(Hanger) in a standard distance.
The rules are:
We should try to place each object in a given standard distance from each other.
There is a max distance from one object to adjacent object which in no way should be violated.
From the start and end also similar standard and maximum distance rule applies.
And there are some portions given where the objects placement needs to be avoided.
I'm not even able to start... which algorithm to use.
If anyone has any suggestion how I can achieve this or some related source please let me know.
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I'm working on a pseudorandom number generator for an assignment and I'm having a hard time wrapping my head around how state is used in it. What does it mean to advance to the next one? I'm not looking for tips on implementation, just an explanation of the concept. Thanks!
A PRNG generates a sequence of numbers.
To calculate the next number, you have some internal state (variables set to specific values, if you will). That's the state referred to in the context of PRNG. This state can often be represented by just a single number.
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I'm doing a project on single precision floating numbers. I was wondering in what fields or areas are these concepts used? Thanks in advance.
For anything requiring larger range than available with integers, and where limited accuracy of number representation isn't important enough to use longer floats. In terms of accuracy, nothing beats integer or fixed point, at the price of their limited range. Say if i wanted cosmological distances in a unit which can be used for both nearer and far objects at the same time, i could think of using those - after all, i'd be mostly interested in the most significant parts of the distance, not in the submillimeter portion.
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Am I correct in saying the energy in the simulated annealing algorithm is equal to the change in cost?
So I can calculate it with the follow:
energy = cost(prevSolution) - cost(currentSolution);
The term 'energy' can have various definitions, but it usually means the current objective value, or the cost of the current state, that is cost(currentSolution).
The difference you defined, along with some transition function, usually specifies the transition probability from one state to another.
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I have number x=[0,n], where n>0.
I want to construct a function y=f(x) such that the value increase slowly from 0 and increase very fast when approaching n, and when reach n, y is infinity. What is a good function to model this?
1/(n-x) - 1/n will work.
There are plenty of other functions log, atan, x^(-k),... that goes to infinity at some point.
a^y is another set of functions with fast grows - maybe more suitable for coding as it can reach arbitrary large (but finite) values.