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

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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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1answer
41 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 ...
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1answer
52 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
22 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 ...
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2answers
59 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
35 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
52 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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41 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 ...
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2answers
64 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
61 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
36 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 ...
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3answers
333 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
167 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
63 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
37 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 ...
3
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0answers
55 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
130 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
34 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
92 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
99 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
75 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, ...
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2answers
109 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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2answers
44 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
99 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
127 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
71 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
29 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
67 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 ...
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0answers
25 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 ...
0
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1answer
40 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
60 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
157 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
90 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 ...
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1answer
110 views

Round-robin pairings: Everybody need to meet everybody

I have the following problem, I have a class of N people and I want them to do stuff by pair, but I want them to do this with everybody but as fast as possible. For N = 4 I got this: ...
1
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1answer
58 views

Simplex method - cycling and condition “>=” or “>” in choice of pivot row

I'm coding the simplex method and observing that it easily falls into cycling, even if Bland's rule is used. It seems to me I have found the reason and I would like to check my understanding is ...
3
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1answer
151 views

Does the limit of $\frac{\partial f}{\partial u}$ at $u=0$ exist?

For an optimization routine I needed to compute the derivative of the right-hand side $\: f_u(x_k, u_k)$ of a discrete-time system $x_{k+1} = f(x_k, u_k)$. Since $\: f_u(x_k, u_k)$ includes terms that ...
3
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2answers
124 views

Disadvantages of adding an extra variable to an optimization problem

Suppose we have an optimization problem $$ \mathbf{x} = (x_1, x_2, \ldots, x_m) = \arg\!\min_{\mathbf{x}\in \mathbb{R}^m}f(\mathbf{x})$$ and a second related problem: $$ \mathbf{y} = (y_1, y_2, ...
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1answer
115 views

How to efficently solve: min $\sum_{ij}(a_{ij}x_{ij}^2 + b_{ij}x_{ij})$ s.t

I am trying to solve the following problem, where $a_{ij} \ge 0 \ \forall i,j$: \begin{align} \mbox{minimize}\quad & \sum_{i=1}^m\sum_{j=1}^n (a_{ij}x_{ij}^2 + b_{ij}x_{ij})\\ \mbox{subject ...
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1answer
97 views

Do you think this p=np workaround worth to try?

I need consultancy for a possible p=np workaround. First of all sorry for my English because it is going to be long question:) To better understand the architecture which I design maybe you will need ...
1
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0answers
75 views

Divide and Conquer division algorithm explained (as used in GMP bignum)

I am trying to understand the divide and conquer division algorithm that is used in the GMP bignum arithmetic library. The code is very optimised and that makes it somewhat hard to understand. the ...
3
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1answer
185 views

What category is this problem?

My first question, please excuse me if its too basic. I have a matrix of evenly spaced geographical points; say 10 x 10, which I will call seed points. Each seed ...