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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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20 views

Using surrogate optimization to reproduce analytical results

I am trying to reproduce results from the following paper: https://www.researchgate.net/publication/261186477_Optimal_design_of_a_novel_tuned_mass-damper-...
24 views

Method for implementing QP solver with matrix terms?

I am trying to implement (in code) a QP solver for the following equation: $$\min_{u} u^{T} Wu$$ $$s.t. \; \beta u = \tau_{ref}$$ $$Au \leq b$$ See this document, section 5.1 (Page 35) $u$ is a ...
59 views

Ramp least squares estimation

With some given $s$ value, let \begin{equation} \begin{aligned} h(\beta)&=\min(\sum_{i=1}^n(Y_i - X_i\beta)^2, s)\\ &=\sum_{i=1}^n(Y_i - X_i\beta)^2-\max(0, \sum_{i=1}^n(Y_i - X_i\beta)...
50 views

Python-accessible industry-standard for unconstrained minimization that converges to machine precision?

I have an unconstrained minimization problem of many variables for which I know the gradient exactly. I turned to the conjugate gradient method contained in ...
45 views

71 views

Pivoted Cholesky vs Modified Cholesky

I am solving nonlinear least squares problems with the normal equations approach, so on each iteration, I need to solve: $$J^T J \delta = -J^T f$$ for the step $\delta$, where $J$ is a large (...
44 views

Finite dimensional optimization problem over dynamical system

I am interested in solving numerically the following mathematical problem Consider an ode of the form $$\dot q(t) = f(q(t),t_1,\ldots, t_N),\qquad t\in [0,T],$$ where $q\in \mathbb{R}^n$ is the ...
94 views

How to solve a 4th order nonnegative LASSO problem?

I need to solve the following 4th order nonnegative LASSO problem: $$\min_{x \geq 0} \quad || |Ax|^2 - b ||^2 + \lambda ||x||_1$$ where $|\cdot|^2$ denotes element-wise squared. $A$ is small size (e....
40 views

Single-variable multimodal derivative-free optimization (for a well-behaved function)

Are there well-established approaches to single-variable multimodal optimization? Given $f:\mathbb{R}\rightarrow\mathbb{R}$ that: has several local minima within a given range of interest $[a,b]$ is ...
60 views

Fast approximate solver for vehicle routing problem

I need to solve capacitated asymmetrical vehicle routing problem with time windows on ~30k points. Time limits for calculations are 2 hours. I've tried using Clarke and Wright savings algorithm, it is ...
71 views

User friendly scipy optimize wrapper package?

I'm creating too much throw away code for interfacing with the scipy optimize package in a user friendly way. (See code below for example of interruptible optimization that keeps last optimization ...
93 views

Why would BFGS converge to a local minima of a non-convex function but maintain a large gradient?

I'm using BFGS to optimize a smooth but non-convex function $f$ that is computed by a simulation. The simulation also gives me a semi-analytical gradient $g$, which is verified by the numerical ...
76 views

How to compute the determinant of Hessian of a multivariable function?

I have a function $F(\vec x)$ of many variables (let's say in the order of hundreds of thousands). I need to compute the determinant of the Hessian matrix at the point $x_0$. Is there a way to ...