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

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Integer programing wth 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
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2answers
50 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 ...
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0answers
40 views

Optimizing Prices with Julia & JuMP [closed]

I'm working on an optimization program (very new to optimization & Julia), and have a toy problem where I'm trying to optimize product prices based on the product price and cross-price elasticity. ...
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2answers
75 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 $R$ ...
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3answers
170 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 ...
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0answers
70 views

Optimization on the manifold of stochastic matrices

So I have an optimization problem of the form $$\text{maximize}\hspace{3mm}f(A):{\bf R}^{K\times K}\rightarrow{\bf R}$$ $$\text{subject to}\hspace{19mm}A^T{\bf 1}=\bf{1}$$ $$\hspace{33mm}A\geq 0$$ ...
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0answers
33 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 ...
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0answers
11 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 ...
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1answer
58 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 ...
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2answers
85 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
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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 ...
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0answers
24 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
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2answers
64 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 ...
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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
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1answer
55 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 ...
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0answers
42 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
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2answers
81 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 ...
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0answers
62 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
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0answers
41 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: ...
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0answers
15 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
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3answers
347 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
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1answer
170 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= ...
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0answers
64 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 ...
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0answers
48 views

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

I have a quadratic problem, \begin{align} \min_{x\in [0,1]^n} x^T p+ \frac{1}{2\lambda} x^T Q x \end{align} ($Q$ is semidefinite) which I want to solve repeatedly, with the slight change of p and Q, ...
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0answers
40 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 ...
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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 ...
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0answers
58 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 ...
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0answers
40 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 ...
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0answers
133 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 ...
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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
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1answer
76 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 ...
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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} ...
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0answers
107 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
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0answers
76 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, ...
0
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2answers
111 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? ...
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3answers
67 views

Symmetric hash function

Can you provide a hash functions $F(x) | F(x) = F(\overline{x}), x \in {\{0;1\}}^n$ $\overline{x} $ is $x$ where all bits are swapped: $0 \rightarrow 1, 1 \rightarrow 0$ Basically it will help me ...
4
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1answer
102 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, ...
5
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0answers
137 views

Best Open Source BLAS / LAPACK package

I was wondering what is a more optimized open source BLAS/LAPACK package with respect to modern multi-core processors (Haswell and beyond). Is there any distribution that can attain performance close ...
0
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1answer
72 views

How to understand what's going wrong in a code for solving a problem with augmented lagrangian?

I am very new to optimization. so, sorry If I ask a simple question. I have a problem with a dozen of variables. I want to use Augmented Lagrangian for solving the problem. I write a code based on the ...
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0answers
30 views

Nonlinear Least Square Regression - Black-Box or LMA Type Methods

In Nonlinear Least Square Regression, is providing errors from all calculated points to the solver like LMA provide any advantage (in terms of speed and number of iterations) over minimizing the sum ...
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0answers
28 views

Optimal distribution of zeros and ones over matrix

I have the following problem: Given a matrix with n rows and m columns. Some elements of the matrix are unavailable. For each column, you have a set containing a number of zeros and ones which must ...
4
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0answers
30 views

Calculus of Variations with unknown cost function but some data

I have a problem that I've framed out in a particular way, but I don't know if I'm re-inventing the wheel here. Is there an existing literature base in this problem? Does it have a corresponding term ...
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0answers
69 views

Problem in using N-BFGS-B in optim

I am a beginner user of R. I am trying to maximize log likelihood function with the bounded parameters. The function is a kind of gamma mixture model which try to ...
0
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0answers
27 views

Implementation in R of $l_2$ penalized weighted quantile regression

I am struggling with such a minimization problem: $$ min_{\mathbf{w}}~~\left( \lambda ||\mathbf{w}||^2 + \sum_{i=1}^{n}v_i |a_i - \mathbf{x_i}^\top\mathbf{w} - b | \right) $$ Here $v_i$ is weight of ...
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1answer
26 views

Benchmark an stochastic constrain solver

I wrote a small simulated annealing library in C++. Right now is just a few classes, a toy project I want to use to test some ideas. But before I move on I want to be sure that it works. Meaning, that ...
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1answer
42 views

Optimizing multiple output parameters for a given input

Problem statement: I'm trying to solve a problem statement using C# as programming language. In the problem system for an input (double/decimal) say $H_i$, the output generated is a form of dataset ...
3
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1answer
62 views

Understanding the conditions for which ADMM can be applied

While reading Boyd's paper on ADMM I encountered an issue. Consider the following problem: Problem. Minimize $f(u) + g(v)$ subject to $Au + Bv = c$, where $f$ and $g$ are closed, proper, convex and ...
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2answers
158 views

Fitting orthogonal planes to a point set

I have a set of 3d points to which I want to fit two planes. I know the assignment of points to the planes so I don't need any RANSAC or similar. Currently, I'm using a PCA-based approach to fit two ...
8
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1answer
93 views

N-body simulation optimisation, looking for name or existing work

during the development of my N-body simulation with visualisation in WebGL, I devised an optimisation, and I'm wondering if it has a name. I find it unlikely that it has never been done before. It ...
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0answers
19 views

optimal SAT solver with weighted variables

I have $n$ boolean variables $x_1,\ldots,x_n$ with associated real-valued costs $c_1,\ldots,c_n$, respectively, and a boolean function $(x_1,\ldots,x_n)\mapsto\Phi(x_1,\ldots,x_n)$ in conjunctive ...