Questions tagged [numerical-optimization]

Numerical methods for continuous optimization.

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Does this adaptive time-step algorithm have a name?

I'm using a somewhat unconventional technique to iteratively minimize a high-dimensional function $E(\vec\theta)$, and have proposed a simple routine to dynamically adapt its time-step. I am seeking ...
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Where can I find a (well-documented) simple solver for linear optimization problems with both equality and inequality constraints?

I need to solve a linear optimization problem subject to both equality and inequality constraints in C++ (using MSVC 15). Mathematically, this can be solved by the simplex algorithm. Since I don't ...
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Find max vectors of a function numerically

I have a function $f(\vec{x})$ that converts a vector to a scalar. $f$ is relatively complex and thus this needs to be solved numerically. Maybe something like gradient descent. I want to find the ...
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Maximizing 3 separate scenarios

I need help with the following business scenario. I’ve tried looking up the math myself, but I realize I was limited on the set up. I believe this will require second order differential equations, ...
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Right algorithm to minimize a function $f(x)$ over grid points $\{x_i\}_{i=1}^{N^n}\subset\mathbb{R}^n$

I want to minimize a uni-modal function (or want to do local-optimization)$f(x)$ over grid points $\{x_i\}_{i=1}^{N^n}\subset \mathbb{R}^n$ when gradient $\nabla f$ cannot be computed. In this case, ...
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Efficient algorithm for determining whether value of convex optimization program is below some value?

Let $X$ be a convex subset of $\mathbb{R}^N$, let $c \in \mathbb{R}^N$. I want to know whether $$\min_{x \in X} x^\top c < 0.$$ Obviously, I can (efficiently, with standard software) evaluate ...
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Is there a way to identify singular points in a spectrahedron without finding the entire set?

I'm a physicist working in a non-linear optimization problem that reduces to a semidefinite program (SDP). In the simple low dimensional cases we workout in the research we could identify singular ...
I would like to find a 19x19 matrix V such that the following inequality holds: $$V^TAV<K$$ and where all entries of V are positive and the sum of entires in a row of V are equal to 1. Also < is ...
I have a stochastic optimization problem where my objective is a piecewise function: $$\underset{x}{\text{min}} \: \sum_{i=1}^{N} E(g(Y, x_{i}))$$ where $Y \sim N(\mu, \sigma^2)$ is a random ...