# 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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### Can the Power Method be used here?

Given a set of $n$ points on which a triangulation is performed, it is possible to construct coefficients $\lambda_{ij}>0$ such that each point $x_i$ is a convex combination of the points connected ...
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### Inconsistency in optimize.minimize

I am trying to fit a time-dependent curve at each time step. I do so in minimizing along $x_c$ the quadratic error between the curve and a reference solution $1/(1 + \exp\left(\sqrt{S}(x-x_c)\right)$...
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A hypergraph $H = (V,E)$ consists of a finite set of vertices, say $V=\{1, \dots, n\}$ and a set of hyperedges $E \subseteq \mathcal{P}(V)$. We call $H$ a $k$-hypergraph if all $|e| = k$ for all $e\in ... 1answer 136 views ### Generate approximately semi-orthogonal tall matrix approximately satisfying constraints I have a set of matrices$\{(A_i,D_i)\}$for$i\in\{1,\ldots,n\}$, where: Each$D_j\in\mathbb{R}^{S\times S}$is diagonal, and every entry on the main diagonal is non-negative. Each$A_j\in\mathbb{R}^...
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I'd like to know whether there are any publicly available tools for solving QCQP with complex variables (and constraints therefore expressed through Hermitian matrices). What I have found so far is ...
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### FMINCON Step Size Tolerance

I get following error after implementing the attached code. Error Message "fmincon stopped because the size of the current step is less than the default value of the step size tolerance but ...
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### How to prevent BFGS from getting stuck on astronomically large gradient?

I have implemented BFGS myself from scratch in order to solve minimization problems. Part of BFGS, as I understand it, is that the approximation to the Hessian is supposed to be positive definite, ...
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### Finding the first N roots of transcendental equation

I need to find the first $n$ roots of the transcendental equation \begin{equation} F(k) = J_m'(kr)Y_m'(k)-J'_m(k)Y'_m(kr) \end{equation} for integer values of $m$ and any $r \in [0,1)$ where $J'$ ...
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### Defining a soft constraint in cvxpy

I am using cvxpy to do a simple portfolio optimization. I implemented the following dummy code ...
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### Nonlinear least-squares solvers vs. generic minimization

A nonlinear least-squares problem with $F:\mathbb{R}^m\to\mathbb{R}^n$, $$F(x) \to \min_x \quad (\text{in the least-squares sense})$$ really means minimizing $$\frac{1}{2} \|F(x)\|^2 \to \min_x.$$ ...
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### What is the fastest way to solve Ax=b (subject to constraints and an absolute term)

I am trying to solve/optimize $Ax=b$ in the least squares sense subject to box constraints; a few (less than 5) equality/inequality constraints; and an absolute function penalty (or some other ...
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### How does the MADS algorithm work in practice

Mesh Adaptive Direct Search (MASH) is an algorithm for black box optimization I want to understand an implement this method to solve some 2D multivariate blackbox function $f(x,y)$, but am having ...
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### What is the most appropriate derivative free optimization algorithm

We can use random optimization/ derivative free/ direct search to find the minimum of some black box function $f$. If I have some 2D black box function, $f(x,y)$ - which I know to be convex - what ...
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### Linear constraints for L-BFGS-B

I know L-BFGS-B only supports simple box constrains of the form: $l_i \leq x_i \leq u_i$, where $l_i$ and $u_i$ are constants. For my specific optimization problem, I need to specify some simple ...
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### How to define the derivative for Scipy.Optimize.Minimize

I am trying to use scipy.optimize.minimize to minimise a quadratic objective function: $f(x) =x^\top Q x$. As a start, I have successfully implemented this using the built-in Nelder-Mead Simplex ...
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### CPU and GPU influence on task parallel execution performance

This question is mainly about hardware, but also about software. In my current work I have approximately 68 millions of combinations that I am iterating through, in parallel. For each of those ...
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### Genetic Algorithm: Need some clarification on selection and what to do when crossover doesn't happen

I'm writing a genetic algorithm to minimize a function. I have two questions, one in regards to selection and the other with regards to crossover and what to do when it doesn't happen. Here's an ...
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### Levenberg-Marquardt for root-finding: just square the function?

This question might be so obvious and trivial that I'm having a hard time googling it. I have a multivariate root finding problem that I'm trying to solve in C# and the library that I'm trying to use ...
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### reduced system: primal-dual interior point method for nonconvex constrained problem

When solving a reduced KKT system of a nonlinear (and nonconvex) constrained program after eliminating slack and dual variables, how do we actually take the next step in a primal-dual method? For ...
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### Procedure to identify characteristic properties of unknown functions in a DAE model

I have a system of 1st order odes given by $$\dot{x_1}(t) = \alpha_1 f_1(x_1,t) + \beta_1 u(t) \\ \dot{x_2}(t) = \alpha_2 f_2(x_2,t) + \beta_2 u(t)$$ They are constrained by an algebraic equation ...
I am solving 1D laplace problem discretized with finite differences (3-point stencil). I would like to use additive Schwarz method in classical form: $U_{k+1}=U_{k}+M^{−1} r_k,$ where $r_k=F−A U_k$...