Questions tagged [mathematical-optimization]

Mathematical optimization deals with maximizing or minimizing an objective function by choosing values from within an allowed feasible set of possible values. Mathematical optimization is often also referred to as mathematical programming or simply as optimization.

Mathematical optimization deals with maximizing or minimizing a real function by choosing values from within an allowed feasible set of possible values. Mathematical optimization is often also referred to as mathematical programming or simply as optimization.

Thus, the study of Mathematical optimization includes formulating the problem (as a set of mathematical equations), and developing several solution techniques. These techniques exploit the underlying structure of the problem. Different optimization algorithms are suited for different types of problems and vary in solution times and computational complexity.

The goal (to be maximized or minimized) is called the "Objective Function." The set of equations that limit the solution space are the "constraints" and the possible solution space is the "feasible region." In some problems, the aim is to just find any acceptable solution, and these are called "constraint satisfaction problems" in which case there is no real objective function to be minimized or maximized.

Broadly, Mathematical Optimization falls under the area of "Applied Mathematics."

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Parallelizing complex and data intensive calculations on the GPU

Preface: I'm sorry that this a very open-ended question, since it would be quite complex to go into the exact problem I am working on, and I think an abstract formulation also contains the necessary detail. If more details are needed though, feel…
Radical
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Mixed Integer Linear Programming to And/Or Constraints

I'm looking to satisfy a set of constraints using PuLP and I'm not exactly sure how to set up the variables to do so. For example, how would I set up variables for the following constraint: ((x_1 < x_2) AND (x_1 < x_3)) OR ((x_1 > x_2) AND (x_1 >…
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Is there any optimization package in J like optim in R?

In J is there a package similar to optim in R?
Bob_Li
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Solving linear program with matrices in CVXPY

I'm using CVXPY in Python 3 to try to model the following linear program in X (N by T matrix). Let R be an N by 1 matrix where each row is the sum of the entire row of values in X. P be a 1 by N matrix defined in terms of X such as P_t =…
Willy
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How to minimize an quadratic objective function with constraint violation using penalty method

I have compared many Quadratic Programming(QP) solvers like cvxopt, qpoases and osqp and found that osqp works faster and better for my application. Now, I want to minimize an indefinite quadratic function with both equality and inequality…
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How to refine the Graphcut cmex code based on a specific energy functions?

I download the following graph-cut code: https://github.com/shaibagon/GCMex I compiled the mex files, and ran it for pre-defined image in the code (which is rgb image) I wanna optimize the image segmentation results, I have probability map of the…
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Finding center point given distance matrix

I have a matrix (really a loaded image) in which every element is a L2 distance from some unknown center point. Here is a trivial example A = [1.4142 1.0000 1.4142 2.2361] [1.0000 0.0000 1.0000 2.0000] [1.4142 1.0000 1.4142 …
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ojAlgo - Expressing Variables as Boundaries in Optimization?

I've been playing around with ojAlgo and I've been pretty thrilled with it so far. I've worked through a few studies with it but I'm having trouble with this problem described in this article. I'm using Kotlin instead of Java, but that shouldn't…
tmn
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Constrained optimization for word2vec giving TypeError

I want to run word2vec model in tensorflow with bounds on embeddings so that they are within unit distance from the origin. That is for every coordinate x in Target and Context matrices -1 <= x <= 1. I found this nice interface that allows one to…
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Linear least-squares solution for 3d inputs

Problem Say I have two arrays with the following shapes: y.shape is (z, b). Picture this as a collection of z (b,) y vectors. x.shape is (z, b, c). Picture this as a collection of z (b, c) multivariate x matrices. My intent is to find the z…
Brad Solomon
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Defining a dynamic function in Python

I'm trying to minimise a function using BFGS method. Initially, I'm creating my functions as expressions. In the first iteration, my first expression is f_sym = ((x0 - x6)**2 + (y0 - y6)**2)**0.5 + ((x0 - x9)**2 + (y0 - y9)**2)**0.5 + ((-x1 +…
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Maximum Likelihood Estimation of a 3 parameter Logarithmic Growth Curve

I am attempting to fit an analytical model to my observed data on human somatic growth. The generalized model is a 3-parameter logarithmic growth curve where: s= B0+B1*t+B2*log(t), where s is a growth parameter whether it be a bone length or…
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A lot sizing model in opl

for my master thesis I have to develope a lot sizing model for a radiology. I implement it with opl and I'm totally new to opl or programming in general. So after a lot of programming time and trying to get the model run, it runs. But now it tells…
CrnD
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OpenModelica and dynamic optmization

I want to test dynamic optimization methods within OpenModelica (the builtin with ADOL-C and the CasADi based). Are there somewhere more information about different options (e.g. change the number of finite elements for collocation, the number of…
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Function "pdist" in Matlab

I have an N by 2 matrix called r (N is very large). r is the position of points in 2D. I searched for the best-optimized way of calculating distance between point. I find that dist function is the best on in less time-consuming if one doesn't try to…
Sonia Sohi
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