FAQ Database Discussion Community

## Constrained quadratic optimization with the quadProg library

r,mathematical-optimization,quadprog,quadratic-programming
I have a vector A of length N. Also I have N*N matrix C. I want to maximize following equation : minimize (- (w_transpose * A) + p * w_transpose * C * w) Where w is a vector of length N, with constraints that each w is non-negative and...

## Is it necessary the two curves are crossing each other if I want to solve two equations with two unknown paramters? [closed]

math,mathematical-optimization,curve-fitting
I have two curves as show in this figure: I have two equations of these curves with two unknown parameters, but I want to know is it necessary for these two curves to cross each other to be solved? or it is not necessary to be crossed? Because I want...

## R optimization with equality and inequality constraints

r,statistics,mathematical-optimization,minimization
I am trying to find the local minimum of a function, and the parameters have a fixed sum. For example, Fx = 10 - 5x1 + 2x2 - x3 and the conditions are as follows, x1 + x2 + x3 = 15 (x1,x2,x3) >= 0 Where the sum of x1,...

## Using sapply (or apply) inside objective function for optim ; object in list element no longer recognized

r,apply,mathematical-optimization,sapply
I would like to use an objective function based on a list of elements, each of which is the result of applying a function over a dataframe (df) ((function is, say, variance of df's observations' "measure")). That is, I have a list of dfs. I naturally want to sapply my...

## How to generate an optimal order of multiple elements based on pairwise element score values

python,optimization,order,mathematical-optimization
I have a number of elements, let say [a, b, c, d], and for each pairwise combination I have a score: [['d-a', 0], ['a-b', 0], ['b-a', 0], ['a-c', 2], ['c-a', 0], ['a-d', 2], ['d-b', 1], ['b-c', 2], ['c-b', 0], ['b-d', 2], ['d-c', 2], ['c-d', 2]] I am looking for a...

## Finding optima of PolynomialFunction in commons.math

java,mathematical-optimization,apache-commons-math
Is there a simple way to find the optimum of a PolynomialFunction (which is also a UnivariateDifferentiableFunction) in commons.math? There are a bewildering array of multidimensional optimizers, but AFAICS the only explicitly univariate optimizer is Brent, which doesn't take advantage of the differentiability.

## Finding a large non-sparse submatrix in a large sparse matrix

algorithm,matrix,mathematical-optimization
I have a very large N x P binary matrix, and I'd like to find two sets R and C which contain the indexes of the rows and columns that make up the largest possible dense (non-sparse, made up of only 1's) submatrix, which meets at least a certain size...

## Matlab: Binary Linear Programming

matlab,matrix,binary,integer,mathematical-optimization
I am trying to solve some equations on Matlab using Binary Integer Programming. I have 3 sets of equations: Ma.X=1 Mp.X<=1 Mr.X<=m* Where, Ma is a known matrix with size 5*12 X is unknown set with size 12*1 Also Mp is known matrix with size 5*12 and Mr is a...

## What is the logic of this process

python,math,while-loop,mathematical-optimization,python-3.4
I was working on a problem in Project Euler; and I found a question in SO. The question and accepted answer says; n = 600851475143 i = 2 while i * i < n: while n%i == 0: n = n / i i = i + 1 print (n)...

## Gurobi in python to calculate lp norm

python,mathematical-optimization,gurobi
Gurobi in python to calculate l1 norm I am trying to calculate l1 norm by using Gurobi in python. Since I am new to python and Gurobi, I am here to ask for help. The model is: minimize 1^T(r+ + r-) s.t. y - X beta = r+ - r-...

## data fitting an ellipse in 3D space

matlab,mathematical-optimization,ellipse,data-fitting
Forum I've got a set of data that apparently forms an ellipse in 3D space (not an ellipsoid, but a curve in 3D). Being inspired by following thread http://au.mathworks.com/matlabcentral/newsreader/view_thread/65773 and with the help from someone ,I manage to get the optimization code running and outputs a set of best parameters...

## Mixed integer programming: variable assignment per condition (if then else)

optimization,mathematical-optimization,linear-programming,scientific-computing,integer-programming
I am relatively new to (mixed) integer programming and got stuck with the formulation of a constraint. In my simplified model I have one Parameter and two Variables that are positive Reals having the value 321 as upper bound. The logic I want to express is here: if Parameter >...

## How to find more clever algorithm to check pairs of primes to see if paired they produce another prime?

ruby,algorithm,primes,mathematical-optimization
I am stuck on Project Euler question 60. I know it is advised not too ask questions or find answers online about it, but otherwise I cannot find the motivation to continue. So I hope to find some help here which can make me go forward. So long for the...

## R function solve.QP error “constraints are inconsistent, no solution!”

r,mathematical-optimization
I am trying to run an optimzation by using the solve.QP function (from the quadprog package) with the following parameters R = matrix( c( 2.231113e-05,-4.816095e-05,-5.115287e-05, 0,2.989584e-05,4.212173e-06,0,0, 5.504990e-05), ncol=3, byrow=T) b = c(-1,0,rep(0,ncol(R))) C = cbind(rep(1,ncol(R)), diag(ncol(R))) C = cbind(-rep(1,ncol(R)),C) d = as.matrix(c(57621264,78057622,171342351),ncol=1) H = solve.QP(Dmat = R, factorized = TRUE,...

## Efficient method of extracting a point from a 3D plane

math,3d,mathematical-optimization,plane
I've come across this method of extracting a location from a 3D plane. I've tested this and it works correctly, but for such a primitive operation, I was wondering if there was a, more efficient method in common practice. void position_from_plane(float r_co, const float p) { const float p_len_sq =...

## Integer programming: assignment of absolute value (depending on variable value)

optimization,mathematical-optimization,linear-programming,scientific-computing,integer-programming
I am relatively new to integer programming and (again) got stuck with the formulation of a constraint. In my simplified model I have a (continous) variable with a lower bound LB below zero and an upper bound UB above zero. Now I want to assign the variable value to other...

## How can I minimize this function in R?

r,function,optimization,mathematical-optimization
I'm attempting to write a formula that will determine a value of a that minimizes the function output myfun (i.e. a-fptotal). MWE: c <- as.matrix(c(.25,.5,.25)) d <- as.matrix(c(10000,12500,15000)) e <- 700 f <- 1.1 tr <- .30 myfun <- function(a) { b <- max(a-e,0) df <- data.frame(u1=c(c*b*.40),u2=c(c*b*.60)) df\$year <- 1:nrow(df)...

## How to convert quadratic to linear program?

mathematical-optimization,linear-programming,integer-programming,quadratic-programming
I have an optimization problem that has in the objective function 2 multiplied variables, making the model quadratic. I am currently using zimpl, to parse the model, and glpk to solve it. As they don't support quadratic programming, I would need to convert this to an MILP. . The first...

## P^N Combinaisons with Integers (Kernel), how to generate them?

java,math,complexity-theory,mathematical-optimization,algebra
My question is almost the same that the one I asked few months ago : 2^N Combinaisons with Integers (Kernel), how to generate them? Basically, I wanted to have the 2^N combinaisons inside a Kernel, but I generalized my version, and now it's even more complicated : I don't want...

## Finding a vector that is approximately equally distant from all vectors in a set

python,vector,linear-algebra,mathematical-optimization,approximate
I have a set of 3 million vectors (300 dimensions each), and I'm looking for a new point in this 300 dim space that is approximately equally distant from all the other points(vectors) What I could do is initialize a random vector v, and run an optimization over v with...

## How to replicate excel solver in R

r,excel,mathematical-optimization
I used excel solver to solve an optimization problem, and I am trying to replicate it in R. I found many packages like optim, ROI etc., but it seems all of them only take a vector as the object to optimize and allow the variables to take any continuous value....

## Fitting circle inside image. Exit condition for loop

python,image-processing,optimization,numpy,mathematical-optimization
I am trying to write some code to check if my circle fits inside a binary mask. So, I have a circle with a given center and a radius. I also have a binary image and I can plot it and see that the circle fits inside the mask. The...

## About correct notation of pareto dominance in optimization

math,mathematical-optimization,genetic-algorithm
I search the correct notation of Pareto Dominance, but i don't know if it is a question for Mathexchange or here.. In multiple papers, like the classic Deb nsga2 paper, you can found the pareto dominance relation written like this A dominate B if In wikipedia, or other paper, like...

## cumulative Distribution function error in indoor localization

matlab,math,mathematical-optimization,indoor-positioning-system
How I'm just wondering if somebody can explain about how can we get the CDF error for indoor localization as in example I found this quote in one of the paper "Usually, the cumulative probability functions (CDF) of the distance error is used for measuring the precision of a system....

## Best way on Java to perform a basic operation with Long [closed]

java,optimization,mathematical-optimization
I have a Long number of 10 digits and I want to now the best way to implement this check. I'll explain it with an example: If we have the number 3456789123: 3 will be multiplied by 10. 4 will be multiplied by 9. 5 will be multiplied by 8....

## R: Isotonic regression Minimisation

r,regression,mathematical-optimization,linear-programming,minimization
I want minimize the following equation: F=SUM{u 1:20}sum{w 1:10} Quw(ruw-yuw) with the following constraints: yuw >= yu,w+1 yuw >= yu-1,w y20,0 >= 100 y0,10 >= 0 I have a 20*10 ruw and 20*10 quw matrix, I now need to generate a yuw matrix which adheres to the constraints. I am...

## R linear model with constraints

r,mathematical-optimization,linear
I want to fit a linear model y ~ a_1 * x_1 + ... + a_n * x_n with parameter constraints a_1,...,a_n >=0 and a_1 + ... + a_n <= 1 in R. Is there an elegant and fast way to do that and without using solve.QP of the quadprog...

## Optimization in R: Maximizing and Minimizing Many Variables

r,ggplot2,mathematical-optimization,minimize,maximize
I have a dataset with 70 foods and information about each food's nutritional value (protein/oz., fat/oz., cals/oz., etc.), as well as the food's cost/oz. I am trying to figure out--given a set budget in \$--what the best combination of foods (and the amt. of each food) would be to maximize...