Questions tagged [optimization]

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

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Is there a high quality nonlinear programming solver for Python?

I have several challenging non-convex global optimization problems to solve. Currently I use MATLAB's Optimization Toolbox (specifically, fmincon() with algorithm=<...
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BFGS vs. Conjugate Gradient Method

What considerations should I be making when choosing between BFGS and conjugate gradient for optimization? The function I am trying to fit with these variables are exponential functions; however, the ...
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What's the fastest software(open source) to solve mixed integer programming problem

I have a mixed integer programming problem. And I am current using GLPK as my solver. But I found that GLPK is good for Linear Programming problem, but for Mixed Integer programming, it requires much ...
11k views

Confusion about Armijo rule

I have this confusion about Armijo rule used in line search. I was reading back tracking line search but didn't get what this Armijo rule is all about. Can anyone elaborate what Armijo rule is? The ...
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Newton-based methods in optimization vs. solving systems of nonlinear equations

I asked for clarification about a recent question about minpack, and got the following comment: Any system of equations is equivalent to an optimization problem, which is why Newton-based methods ...
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Pressure as a Lagrange Multiplier

In the incompressible Navier-Stokes equations, \begin{align*} \rho\left(\mathbf{u}_t + (\mathbf{u} \cdot \nabla)\mathbf{u}\right) &= - \nabla p + \mu\Delta\mathbf{u} + \mathbf{f}\\ \nabla\cdot\...
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Solving a least squares problem with linear constraints in Python

I need to solve \begin{alignat}{1} & \min_{x}\|Ax - b\|^2_{2}, \\ \mathrm{s.t.} & \quad\sum_{i}x_{i} = 1, \\ & \quad x_{i} \geq 0, \quad \forall{i}. \end{alignat} I think it is a ...
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Efficient solution of mixed integer linear programs

Many important problems can be expressed as a mixed integer linear program. Unfortunately computing the optimal solution to this class of problems is NP-Complete. Luckily there are approximation ...
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How is geometric programming different from convex programming?

How is (generalized) geometric programming different from general convex programming? A geometric program can be transformed into a convex program, and is typically solved by an interior point method....
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Calculating Lagrange coefficients for SVM in Python

I'm trying to write a full SVM implementation in Python and I have a few issues computing the Lagrange coefficients. First let me rephrase what I understand from the algorithm to make sure I'm on the ...
680 views

Trace An Isoline of an Expensive 2D Function

I have a problem similar in formulation to this post, with a few notable differences: What simple methods are there for adaptively sampling a 2D function? Like in that post: I have a $f(x,y)$ and ...