# Tagged Questions

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

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### Approximating rotation matrix of arbitrary objective function

I want to approximate the rotation in SO(3) (ie. 3D rotation) that minimizes some objective function. I'm looking for a SO(3) rotation representation that lends itself to energy minimization. I'm ...
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Is it pointless to use gradient based optimization algorithms if you can only provide a numerical gradient? If not, why provide a numerical gradient in the first place if it is trivial to perform ...
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### Methods to Estimate Optimal Distance Measure for Multidimensional Data Set

My problem at hand pertains to choosing a distance measure for use in locally weighted regression. In my particular problem, I have a data set that is upwards of 10 dimensions, where the variables ...
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### Vectorizing list of different functions for Gradient Descent

I am new to machine learning and statistical analysis and am having trouble figuring how I should go about a problem I have. I believe that I understand the gradient descent algorithm and how it ...
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### imposing “measured data” to Dirichlet boundary conditions in fenics

I'm relatively new to fenics and I just looked through all questions related to Dirichlet boundary conditions. I don't seem to find a well-described question or answer about what I'm about to ask. I'...
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### From deterministic to stochastic LP formulations

I am having a hard time understanding the very first example in "A Tutorial on Stochastic Programming". More specifically the authors show that one can formulate the stochastic variant of (1.2) ...
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### Finding quick solution to a collection of systems of fairly simple but nonlinear equations

So I have a collection of systems of equations, basically $n$ systems of equations, each composed of $k$ equations: $$\frac{a_1x_{1j}}{a_1x_{1j} + \cdots + a_kx_{kj}} + \log x_{1j} + 1 - B_{1j} = 0$$ ...
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### Choose of basis set [closed]

I am engaged with the syntheses and DFT calculations of coordination complexes. I wonder how can I set up the basis set for carried out using B3LYP method and mixed basis sets of LanL2DZ for Pd and 6-...
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### How to optimize interaction of flexible 3D shapes in space/what is this technique called

I am not sure what terminology I should use here or even what field this is. That information itself would be incredibly helpful, this is new territory for me. I'm trying to figure out how to solve ...
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### Conservative Short Sales Portfolio Optimization with MatLab code help

I'm trying to solve the optimization problem below with MatLab, but I'm unsure of how to modify the constraints in the quadprog function (or how to add the constraints with the Portfolio object). In ...
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### Problem with Levenberg-Marquardt for FEMU case

I m trying to implement a Levenberg-Marquart on python to identify 2 material parameters via Finite Elements calculations and full-field measurements as called FEMU (Finite Elements Model Updating). ...
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### GSA Search Algorithm in C++

Is there any version of GSA (Gravitational Search Algorithm)[1] implemented with C++ or even C#? What I found was implemented using MATLAB which is not good for me. [1] Rashedi, Esmat, Hossein ...
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### NONLINEAR ENERGY MINIMIZATION EXAMPLE

I am learning about FEM methods and nonlinear optimization. I would like to try my nonlinear trust region solver on some simple nonlinear problem. What would be good example to implement for ...
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### Integer programming with Matlab

I'd like to know how to solve in MATLAB the following integer optimization problem : $\underset{B,D}{\arg\min} \Vert{Y-XDB}\Vert_{2}$ where $X,Y$ are given matrices. The constraint is the following ...
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### Fitting rectangle to segments in image

I have the task to fit a rotated rectangle of known size into an image like This is a synthetic test case, in the real application, everything is rather blurred. The rectangle has to cover as much ...
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### What kind of optimisation algorithm is suitable for a computationally expensive function?

I have a reference value $R$ and a modelled value $M$. $M$ is generated using a stochastic algorithm with parameters $a$ and $b$. The objective is to tune $a$ and $b$ so that $M$ is as close as $R$ ...
201 views

### why non-convex optimization should be a problem?

I was very surprised when I started to read something about non-convex optimization in general and I saw statements like this: Many practical problems of importance are non-convex, and most non-...
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### Optimization on the manifold of stochastic matrices

So I have an optimization problem of the form $$\text{maximize}\hspace{3mm}f(A):{\bf R}^{K\times K}\rightarrow{\bf R}$$ $$\text{subject to}\hspace{19mm}A^T{\bf 1}=\bf{1}$$ $$\hspace{33mm}A\geq 0$$ ...
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### lbfgsb quit at the first iteration

Recently I've been working on the implementation of an algorithm, which need me to solve a bounded optimization problem with quality constraints. So I downloaded a Matlab wrapper for lbfgsb. It is L-...
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### Is casadi suitable for data fitting?

Quite often I do fit some ODE or DAE systems to my data (small to medium sized problems). Via the assimulo package, I found Casadi and read a bit about the language modellica. Casadi offers automatic ...
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### Repeated 1d minimization with similar parameters (scipy)

I have a function f(x,k1,k2) and I am trying to minimize it over x for different values of ...
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### On Boyd et al.'s convergence analysis of ADMM: Why do we need the convexity assumption?

Please refer to Boyd et al.'s convergence analysis of ADMM (Chapter 3 and Appendix A). My question is: Why do we need $f$ and $g$ to be convex? I don't see the need of this assumption. If the ...
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### Divide and conquer for optimizing weakly unimodal continuous function?

Is there a divide and conquer algorithm for optimizing weakly unimodal continuous functions? Adding more details: My function has a flat line on the left and right and then there is a global ...
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### Will Golden Section Search work for optimizing weakly unimodal functions?

Will Golden Section Search work for optimizing weakly unimodal functions? If not is there any variation of it that will allow for optimizing weakly unimodal functions instead of strictly unimodal ...
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In these notes (section 2.3), it is stated that: A point $x^*$ is a minimizer of a function $f$ (not necessarily convex) if and only if $f$ is subdifferentiable at $x^*$ and $0 \in\partial f(x^*).$...
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### MINPACK implementation in Fortran77 code

I am using LMDIF1 subroutine of MINPACK Library for curve fitting. The external subroutine fo6in LMDIF1 is the program that I want to use for curve fitting and was ...
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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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### About training HMM by using EM

I am new to EM algorithm, studying Hidden Markov Model. During training my HMM by EM, I am very confused on the data setting. (text processing) Please confirm whether my EM usage is okay or not. At ...
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### Which C++ Multi-objective Optimization libraries allows the addition of custom problems and custom algorithms?

I'm working on a custom discrete and constrained multi-objective optimization problem and I'd like to know which libraries or platforms that implement algorithms like ...
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### Need help writing the code for the following optimization

I need to find $X$ for which the following expression is minimized: $$\min ||Y - F^{-1}(X)||_2 + ||X||_1$$ where $Y$ is an array (of length approx 44000, an audio sample I will be reading using ...
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### Mobile robot path following using model predictive control (MPC)

I'am trying to implement a path following algorithm based on MPC (Model Predictive Control), found in this paper : Path Following Mobile Robot in the Presence of Velocity Constraints Principle: ...
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### How to solve a model with a quadratic term in the objective function on CPLEX?

I introduced a model with a quadratic objective function in CPLEX but it takes a long time to solve it, I think there is a way to tell CPLEX that the model has a quadratic objective function, but I ...
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### Scientific Programming Contests

I regularly compete in so called "Programming Contests", where you solve difficult algorithmic problems with your own code and problem solving skills during a limited time-frame. For referential ...
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### Preconditioned Conjugate Gradient linear system solver in MATLAB

I have been trying to use the MATLAB's pcg() function to minimize an energy functional. Converting minimization problems to the solution of a linear system is ...