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

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5
votes
2answers
45 views

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 ...
9
votes
3answers
280 views

Is providing approximate gradients to a gradient based optimizer useless?

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 ...
6
votes
0answers
55 views

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 ...
1
vote
1answer
73 views

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 ...
9
votes
1answer
124 views

Adaptive gradient descent step size when you can't do a line search

I have an objective function $E$ dependent on a value $\phi(x, t = 1.0)$, where $\phi(x, t)$ is the solution to a PDE. I am optimizing $E$ by gradient descent on the initial condition of the PDE: $\...
1
vote
0answers
23 views

Difference between Chebyshev first and second degree iterative methods

Consider linear equation $Au = f$. We want to solve it with iterative method (assuming $A$ is good). First order iterative method is: $$ u^{k+1} = u^k - \alpha_{k+1}(Au^k - f), $$ The second degree ...
0
votes
0answers
30 views

Weighted Frobenius norm in BFGS

In what sense is the weighted Frobenius norm "adimensional"/"scale-invariant" for any symmetric positive definite weight matrix $W$? If we plug in a positive diagonal matrix into $W$ wee see that $||A|...
1
vote
1answer
38 views

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'...
3
votes
1answer
42 views

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) ...
4
votes
2answers
75 views

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: $$\frac{a_1x_{1j}}{a_1x_{1j} + \cdots + a_kx_{kj}} + \log x_{1j} + 1 - B_{1j} = 0$$ ...
1
vote
0answers
66 views

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-...
0
votes
0answers
30 views

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 ...
1
vote
0answers
40 views

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 ...
0
votes
0answers
29 views

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). ...
1
vote
2answers
90 views

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 ...
0
votes
1answer
39 views

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 ...
0
votes
1answer
86 views

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 ...
2
votes
2answers
63 views

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 ...
2
votes
2answers
87 views

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 $R$ ...
9
votes
3answers
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-...
5
votes
0answers
140 views

Optimization on the manifold of stochastic matrices

So I have an optimization problem of the form $$\text{maximize}\hspace{3mm}f(A):{\bf R}^{K\times K}\rightarrow{\bf R}$$ $$\text{subject to}\hspace{19mm}A^T{\bf 1}=\bf{1}$$ $$\hspace{33mm}A\geq 0$$ ...
0
votes
0answers
37 views

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-...
1
vote
0answers
12 views

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 ...
1
vote
1answer
60 views

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 ...
0
votes
2answers
90 views

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 ...
0
votes
1answer
54 views

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 ...
0
votes
0answers
25 views

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 ...
4
votes
2answers
68 views

Subgradients of non-convex functions

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 $0 \in\partial f(x^*).$...
0
votes
0answers
36 views

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 ...
4
votes
1answer
59 views

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 ...
0
votes
0answers
44 views

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 ...
1
vote
2answers
120 views

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 ...
0
votes
0answers
64 views

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 ...
4
votes
1answer
51 views

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: ...
0
votes
0answers
16 views

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 ...
14
votes
3answers
357 views

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 ...
5
votes
1answer
175 views

Solving a set of linear equations with block structure and weak coupling

I have a standard set of linear equations $Ax=b$ where the Hessian matrix $A$ has the special block structure as shown: $A= \begin{pmatrix} T & U\\ U^T & V \end{pmatrix}$, $x= \begin{...
2
votes
0answers
66 views

Solving a nonlinear poisson equation via variational minimization

I am kind of new in finite elements and I am solving simple "Poisson nonlinear" problem. $- \nabla ((1 + u^2) \nabla u) = f$ $u = 0 \ \text{on} \ \Omega $ I am using Newton solver, where I have ...
1
vote
1answer
70 views

What is the fastest method for solving a quadratic programm repeatedly,( warmstarted)?

I would like to solve the following optimization problem \begin{align} \min_{x\in [0,1]^n} x^T p+ \frac{1}{2\lambda} x^T Q x \end{align} $Q$ is a positive semidefinite matrix. $\lambda>0$ is a ...
1
vote
0answers
46 views

Scaling a vector-valued non-linear function for numerical optimization/minimization

I am trying to minimize a non-linear vector-valued function in MATLAB. As a test case for my code, I try to minimize a function whose solution I know apriori. The problem is that one of the ...
0
votes
0answers
20 views

Ordering of eigenvectors to maximise trace of diagonalising matrix

I asked a similar question on the Mathematics stack exchange here without much success, so I thought I'd ask it with a more practical bent here. Suppose we have a Hermitian matrix $H$ with (for the ...
3
votes
0answers
60 views

Best way to add a positivity constraint to Newton's Method

So given an objective function $f({\bf x})$, I would like to include a positivity constraint when I perform the fixed point iteration: $${\bf x}^{(t+1)}={\bf x}^{(t)} - \text{H}_f^{-1}\nabla f({\bf x}^...
1
vote
0answers
44 views

Exact line Search in Steepest descent

I wanted to clarify the idea of the exact line search in steepest descent method. An exact line search involves starting with a relatively large step size ($\alpha$) for movement along the search ...
0
votes
0answers
139 views

how to solve a 2D non-linear Poisson equation?

I am trying to solve the following equation for $P(x,y)$: $$I = P \nabla \cdot \frac{1}{P^2} \nabla{P}$$ where $P$ and $I$ are functions of x and y. $I(x,y)$ and $P(x,y)$ I want to understand ...
1
vote
1answer
35 views

limiting function as cost function: logistic function between -a and +a

I would like to fit a diffusion coefficient as function of e.g. salt, pH etc. If I use a linear combination of all variables, I will have to apply constraints because the model fails, if the diffusion ...
1
vote
1answer
78 views

Fit curve with rectangles

I have a one-dimensional set of points, i.e. $(n,y_n), 1\leq n \leq N$. I want to fit them with a linear combination of $k$ rectangular functions in a least-squared-error sense. Each rectangle is ...
1
vote
1answer
93 views

Can this equation be solved with the conjugate gradient method?

Let $A$ be positive-definite and $C$ diagonal positive-definite, consider the problem of solving the following equation for $\bf x$ $$A{\bf x}+C\begin{bmatrix} e^{x_1} \\ \vdots \\ e^{x_n} \end{...
0
votes
0answers
116 views

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 ...
3
votes
0answers
78 views

Striking examples of success of local search algorithms

In N queens problem https://en.wikipedia.org/wiki/Eight_queens_puzzle, trying to find solution by backtracking encounters difficulties quite fast (even for SWI-Prolog, http://swish.swi-prolog.org/...
0
votes
2answers
116 views

What method do you suggest to solve this minimax, quadratic in both variables problem?

I have a problem of the form, \begin{align} minimize_{y} maximize_{x}&\quad x^T y - y^T (B\odot x x^T) y\\ s.t. &x\in [l,u]\\ &Ay=b \end{align} How to efficiently solve this problem? ...