# Questions tagged [optimization]

This tag is intended for questions on methods for the (constrained or unconstrained) minimization or maximization of functions.

725 questions
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### Algorithm design to filter on 5,000 stocks each of which has 4 months worth of data points

I want to filter on 5000 stocks, each of which has 4 month or more worth of data (>= 500 data points each). my filtering criteria will be based on 8 calculated values from the data points. for example,...
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### Why can't we discretize continuous domains in distributed non-convex constraint optimization problems?

Consider a non-convex distributed optimization problem. We have $X$ = a set of $n$ decision variables: $x_i$ where $i=1..n$ and $x_i \in R$, the set of Reals. We have $F$ = a set of $m$ constraint ...
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### Linear regression with inequality constraint in Java

I haven't been doing math in years and I'm facing the following problem. I'm trying to implement in Java a linear regression under a set of inequality constraints. Sorry in advance for all the ...
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### Robust/Tested Solver for incompressible 2D Euler (Fluid dynamics) Equation

I am trying to locate suitable computational algorithms for a optimization problem that requires repeated solution of transient 2D incompressible Euler equation on a 2D domain (say rectangular). My ...
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### Why do active set methods or the simplex method pivot only one variable at a time?

Why do active set methods or the simplex method pivot only one variable at a time? Ostensibly, we could add multiple columns to the basis during pivoting, but the standard presentation of the methods ...
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### Optimal Control using Dynamic Programming - Optimizing for Furthest Distance

So I have been investigating a problem to get a glider with control of its elevator to fly as far as possible from any given initial state. To keep this simple, we will view this in 2D space with the ...
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### Solving multiple least-square problems with the same constraints

The following least-square problem can be solved efficiently (e.g. using matlab's lsqlin): $$\vec{x}^*=\arg\min_\vec{x} ||C\vec{x}-\vec{t}||^2\,\ s.t.\ Ax \le \vec{b}$$ where the parameters of the ...
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### What is the most intuitive explanation for the concepts of weak local minimizer, strong local minimizer and isolated local minimizer?

Reading Nocedal's book on optimization, I came into the concept of local minimizer, which is a well-known concept in numerical optimization. However, I think I am having a rough time trying to come up ...
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### Quadratic programs with rank deficient positive semidefinite matrices

Let $A$ be a $n\times n$ square symmetric matrix. In addition, $A\succeq0$ and $\mathrm{rank}(A)<n$. This means that all eigenvalues are non-negative, but also that there are some zero eigenvalues. ...
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### energy computation for BVP with Dirichlet boundary conditions

I am solving quadratic minimization problem \begin{align} \min_{x}\ \frac{1}{2} x^T A x -b^T x, \end{align} where matrix A results from discretization of Laplacian by FEM method, subjected to ...
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### What are the differences between the different gradient-based numerical optimization methods?

I am interested in the specific differences of the following methods: The conjugate gradient method (CGM) is an algorithm for the numerical solution of particular systems of linear equations. The ...
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