# 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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### Robust optimization using fmincon in Matlab?

I am trying to implement the following optimization (from this paper) in Matlab using fmincon: $\min_\omega\omega'\Sigma\omega$ subject to $\min_Ur_p \geq r_0$ where $\Sigma$ is a positive definite ...
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### Literatures on numerical stability of optimisation algorithms

I am curious of whether optimisation algorithms (whatever simplex, active-set quadratic programming, interior point sequential etc.) can fail due to numerical errors and how to avoid them. But I ...
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### Simple bound constrained optimization problem

My problem is $$\text{minimize}: \phantom{2} f(x) \\ \text{subject to }: \phantom{2} x_4 \ge 0$$ where $x=(x_1,x_2,x_3,x_4)$. I know that the fourth component $x_4$ of the desired local minimizer ...
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I encounter an optimization problem. The simplified version is like following: Denote function $F(x):\mathbf{R}^n\rightarrow\mathbf{R}$, where $F(x)$ is a smooth lower bounded convex function (i.e. ... 2answers 188 views ### non-convex quadratic with only one quadratic constraint? I have a non-convex optimization problem in the form: \begin{align} \min_{b,\xi,\eta} \sum_{i=1}^{n} b_i \xi_i + \gamma \Vert \eta \Vert \cr \text{s.t.} b\geq 0, b^\mathsf{T} 1 = 1,b_i \leq \frac{1}{n-... 1answer 343 views ### Does the amount of correlation of model parameters matter for nonlinear optimizers? I am using nonlinear optimizers such as BOBYQA to train a model with 10-20 parameters. It so happens that some of the parameters have high correlation. Roughly speaking, imagine that you are fitting ... 1answer 234 views ### constrained minimization in N dimensions I am looking to create an algorithm to minimize an N dimensional problem. I am unsure how to write it in its generic form, so I will show it in 1, 2 and 3 dimensions Minimize \sum_{i} x_i\left [ f\...
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I've got a function of form $$f: (\mathbb{Z}_3)^n \rightarrow \mathbb{R}$$ to optimize, where $n$ is relatively large (the order of hundreds). Is it there a gradient-like notion for these type of ...
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### How to avoid NaN in optim?

Suppose, I have a function and want to optimize it. But if I use optim() which gives warnings(). How can I avoid these warnings ...
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### Second order directional derivative in image processing

it is all about valley detection in image processing. I would like to find, for a given pixel, direction for higher second order derivative. I am not quite sure what discrete mask/filter I can use to ...
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I am reading the following file, that explain the Nelder-Mead optimization Algorithm.(Algorithm Below) Where $B$ is the best point, $G$ second best point, $W$ is the worst point, $R$ reflection point. ...
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### Should I include integral constraints in a integer linear program with a totally unimodular constaint matrix?

I have formulated an integer linear program (ILP). The constraint matrix for the ILP is totally unimodular. Should I solve it as an LP without the integral constraints, or should I keep the integral ...
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### Which optimization method can be used to do the following?

I've the following system of equations for studying information flow in the below graph, $$\frac{d \phi}{dt} = -M^TDM\phi + \text{noise effects} \hspace{1cm} (1)$$ Here, M is the incidence ...
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### Can I solve a model in GEKKO with Black Box, Simulated Annealing or GA solvers?

I'm trying to use my current GEKKO model with different solvers methodologies. I don't know if I can also use global optimisation solvers as GA, Simulated Annealing o Differential Evolution. I need ...
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### Examples of problems that cannot be formulated as optimization problems

An optimization problem has 3 main components: decision variables, constraints and an objective function. Such a problem can be mathematically modelled and solved using an optimization solver. For ...
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### How does fmincon in MATLAB calculate gradients?

I am trying to solve numerically a constrained optimisation problem in MATLAB, and I am wondering how the fmincon function calculates gradients when one isn't ...
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I'm currently trying to minimize the following function: $$\min_{\mathbf x,\mathbf y,s} \|F\mathbf x-\mathbf a\|_2^2 + \|SF\mathbf y-\mathbf b\|_2^2 + \lambda \|\max(\mathbf x, \mathbf y)\|_1,$$ $$\... 1answer 157 views ### Optimization of non-smooth, non-convex, locally Lipschitz functions of type exp(-abs(x)) What would be the numerical method of choice to find minima in a non-smooth, non-convex, locally Lipschitz function f: \mathbb{R}^n\rightarrow \mathbb{R}. The function f is mostly smooth but ... 1answer 133 views ### Efficient way to generate a list of possible matrices (all integer components) with a determinant V I have an interesting problem from my research that I have been struggling to solve. One part of the problem involves generating all possible matrices, where each set contains three integer vectors, ... 1answer 364 views ### Sum of Inverse of Variables in an Optimization Problem I have the following optimization problem:$$ \begin{array}{ll} \text{Minimize} & \frac{1}{x_1} + \frac{1}{x_2} + \ldots + \frac{1}{d_n} \\ \text{Subject to} & A x \leq b \end{array} $$where ... 1answer 61 views ### Iteratively refine bounds on exp for Metropolis criterion In Monte Carlo simulations, using the Metropolis criterion, one often has to compare a random number a, 0 \leq a < 1, to the Boltzmann distribution exp(-\beta\Delta E), where \Delta E is ... 3answers 168 views ### Plane constraints in R3 I have multiple plane constraints in \mathbb{R}^3 of the form:$$n_i \cdot x \ge \delta_i Where $n_i$ is the $i$th plane normal (in form (x, y, z)), $x$ is a point in space, and $\delta_i$ is ...
I have a cost function: $f(x,y,z) \rightarrow \mathbb{R}$ it is very expensive to evaluate $x,y,z \in \mathbb{Z}$ 0 < x < 10 0 < y < 30 0 < z < 100 I thought it was convex, not sure ...
I have a numerical problem in which I need to find the values $\lambda$ for which the determinant of a matrix $A_\lambda$ is zero. (The solutions $\lambda$ will give the eigenvalues of an operator...) ...