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

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25 views

CPLEX in MATLAB - Asking for Help

I am using CPLEX in MATLAB. I want to optimize the following function $$\begin{align} &\min \Vert y\Vert\\ &\Vert y\Vert = \sum |y|\\ &\text{subject to } A y = 2B - A\, 13n \end{align}$$ ...
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0answers
20 views

Interpolation of Data Value using Optimized Weighting of Its Features

Assume I have a data set $ { \left\{ {x}_{i} \right\} }_{i = 1}^{N} $ which represents the value of each data point. For each data we have its features $ {f}_{i} \in {\mathbb{R}}^{d} $. The model I ...
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1answer
50 views

Direct multiple shooting (numerical optimal control)

please, Iam currently implementing direct multiple shooting method* and I need one simple but fundamental concept answered: When I want to provide not only objective funtion value (result of ODE ...
4
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3answers
107 views

Objective function scaling in an Inverse Problem

I am trying to solve a large scale inverse problem using the Bayesian formulation. To estimate the Maximum a Posteriori Estimation (MAP) solution I will have to minimize the following objective ...
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0answers
30 views

Graph optimization for parallel processing

Consider the following example structure of overlapping images marked A,B,C,D. The possible overlaps are marked by gray color: The structure can be represented by a weighted undirected graph ...
4
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3answers
107 views

Minimization of non-linear function

Problem Summary I am trying to estimate the (x,y) coordinates of each node in a graph, where I know the distances between connected nodes. For example Given this ...
-1
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1answer
56 views

Problem using MATLAB `fminunc` [closed]

I am trying to find the minimum of this function. But I receive the following error when I run the script. What am I doing wrong: ...
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0answers
27 views

Find the set of K elements between n that maximize the total distance

Given a set $Q$ of $n$ points, we want to find the subset $S_\max \subset Q$ of $k$ elements that maximize the total distance between them. $$S_\max = \max_S \sum_{\substack{ i,j\in S\\ i \neq j}} ...
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0answers
51 views

Fitting high frequency trading model

I have a high frequency time series of the bid and ask prices of a stock recorded on every tick. For each data point I also have a certain indicators that predict the future movement of the price. The ...
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2answers
114 views

Selecting most scattered points from a set of points

Is there any (efficient) algorithm to select subset of $M$ points from a set of $N$ points ($M < N$) such that they "cover" most area (over all possible subsets of size $M$)? I assume the points ...
2
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1answer
106 views

Solve $AX = B$ where $X^T X = C$

Is there a natural way to find the solution to $$AX = B, X^TX = C \enspace \text{?}$$ $X$ is a matrix and has a small number of rows, and $A$ is sparse. An approximate solution would be fine.
3
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1answer
80 views

Trust-region Newton: implementation issue with Conjugate Gradient calculations

UPDATE: The problem turned out to be the step (refer penultimate paragraph below) where I was factoring out a small value from the vectors of the numerator and denominator and then computed dot ...
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1answer
30 views

Converting linear BIP constraints into convex hull

Given a linear BIP $$\text{Minimize}\;\;\;c^Tx$$ $$\hspace{6.5mm}\text{Subject to}\;\;\;Ax\leq b$$ $$\hspace{38mm}x\in\{0,1\}^n$$ We can in theory convert the constraints to the convex hull ...
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0answers
55 views

Simple MCMC Algorithm in Matlab

I would be really glad to get some specific advise on how to implement a simple MCMC algorithm (in Matlab, if possible). I'm not yet too familiar with optimization methods. My problem goes as follows: ...
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2answers
59 views

Solving absolute value quadratic optimization problem

would you please help me to solve following problem $$x^*= \text{argmin}\ xLx^T+ |P^Tx|$$ $x$ is binary $P$ is a known vector (with positive and negative values) $L$ is Laplacian matrix I have ...
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0answers
28 views

Cyclic Coordinate Descent Optimization for Bayes Logistic Regression (Code Problem?)

I am trying to reproduce the CLG algorithm for the Laplace prior given in Genkin et al to find the MAP estimates for a logistic regression model. I am using Python (Anaconda 2.2) with Numpy to ...
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2answers
117 views

Ideas on how to search nearby geospatial data fast

I am looking at a very simple problem, but can't quite find the best solution. I need to accept a lat/lon coordinate and based on that coordinate find all the points within roughly ~1km (accuracy is ...
5
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2answers
154 views

Python solvers for mixed-integer nonlinear constrained optimization

I want to minimize a black box function $f(x)$, which takes a 8$\times$3 matrix of non-negative integers as input. Each row specifies a variable, whereas each column specifies a certain time period so ...
2
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1answer
44 views

scaling and preconditioning for trust region Newton methods

Geometrically, scaling and preconditioning seem to address similar challenges in optimization. However, these two concepts are implemented very differently. Take trust region Newton method, as an ...
3
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2answers
75 views

Derivative-free optimization of function with a flat region

I'm attempting derivative-free minimization of, essentially, a black-box function in one dimension. Up to now I've been using BOBYQA as implemented in NLopt. The shape of the function looks like this: ...
3
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0answers
30 views

Python trust region optimization code that allows ellipsoid-shaped trust regions

Are there any high quality trust region optimization implementations that allow nonspherical ellipsoid trust regions, and are written in Python, or are easy to call from python? By nonspherical ...
3
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2answers
67 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 ...
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1answer
57 views

Converting smooth $L1$ norm approximation into SOCP

I am approximating the expression $\left\|Ax-b\right\|_1$ by the expression $$\text{minimize}\;\;\sum_i\sqrt{(a_i^Tx-b_i)^2+\varepsilon}$$ where $a_i$ is the $i^{th}$ row of $A$. This function is ...
0
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1answer
44 views

What are open source codes for interior point optimization to modify?

I am working on a modified interior point algori thm for semidefinite for my special problem. I don't have enough skills and knowledge about interior point for semidefinite to code it from scratch. ...
3
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2answers
119 views

Solution to the optimization problem in “Blessing of Dimensionality High … the face verification”

I am reading the work "Blessing of Dimensionality High dimensional feature and its efficient compression for the face verification" CVPR 2013. One of the key contributes is the authors propose a new ...
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1answer
23 views

Approach to determining most likely integer factors of a noisy measurement?

I have a quantity which is estimated from a number of noisy measurements. I know that the real underlying value must be some integer multiple of two quantities, e.g. $M = I_1C_1 + I_2C_2$ where $C_1$ ...
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1answer
36 views

How to nest 2 simple CVX problems? Is it possible at all?

I have the underdetermined outer optimization problem $$\text{min}_{x\geq 0}\quad \|Ax-b_1\|_2^2+\|AT(x)-b_2\|_2^2$$ with $A\in\mathbb{R}^{m\times n}$ and $m<<n=64^2$ or in corresponding CVX ...
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2answers
125 views

Find $\min \sum_{1\le i\le n} x_i\mathbf{z}^T\mathbf{A}\mathbf{y}_i +\mathbf{b}^T\mathbf{x} +\cdots$

I have been stuck at this problem for a while :( Given $\mathbf{A}\in\mathbb{R}^{p\times p}, \mathbf{A}\ge 0,\mathbf{A} \text{ symmetric}, \mathbf{b}\in\mathbb{R}^n,\mathbf{c}_i\in\mathbb{R}^p\forall ...
2
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1answer
80 views

Hessian-free and Truncated Newton methods

In this paper on Deep Learning for Machine Learning, the approach is referred to as Hessian-free method. That is because the Hessian is never computed explicitly. Instead, the product of the Hessian ...
0
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1answer
91 views

Use line segments to approximate a function

I need to use line segments to approximate a function, f = 1/x. The range of x is from 1 to 2048 with an interval of 1. I will pick 10 locations for x and interpolate y between two adjacent x using ...
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0answers
33 views

Optimization of nonlocal stencil-like operator on subset of regular grid

I am trying to optimize the execution time for this particular piece of fortran code. Details: i_gc is a (ngpts, 3) array of containing (i,j,k) indices for each grid point. This is a subset of the ...
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0answers
37 views

Numerical Implementation of “integrates to some values” type constraint in convex solvers?

I am maximizing a linear functional subject to an integrates to one constraint. More explicitly, my problem is $$\begin{align} &\max_{x \in \mathbb{R}^n}\quad c \cdot x\\ &\text{subject to} ...
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0answers
46 views

Is there a convergence proof for ADMM applied to biconvex/bilinear problems?

Ok, I've already asked this question in math.stackexchange, but I feel it is more appropriate to ask here (hopefully I am not violating any rules by repeating!). So here it is: I wonder if there ...
1
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1answer
59 views

Gradient Descent

I am working with an objective function that is convex globally, but the path downward is lined (if you will) with quartz crystals. In this case, the update vector (gradient solution) of partial ...
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0answers
36 views

How to scale variables for optimization if one of them is an exponential

I do use scipy`s leastsqare function for data fitting. My function looks like: $$ \frac{dy_i}{dt} = K_{kin} *x_i* (K_2 * (K_2 - a*y_i - b*y_i)^c) - y_*cs^c ) $$ The variables are ...
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3answers
105 views

Dealing with errors in non-linear least square problem

I am currently working with a optimization problem involving a non-linear least square problem. I have chosen to use lsqnonlin in Matlab. What follows is a ...
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0answers
86 views

Frank Wolfe algorithm in matlab

I'm trying to solve the following question : $$ maximize \ x^{2}-5\cdot x + y^{2}-3\cdot y $$ $$ x+y\leq 8 $$ $$ x\leq2 $$ $$ x,y\geqslant 0 $$ By using Frank Wolf algorithm ( according to ...
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1answer
44 views

Solving nonlinear optimization problem with combinational constraints

I have to minimize a nonlinear objective function $f(x_0, x_1, x_2, x_3, x_4, x_5)$ with 6 variables. The constraints governing these these variables are a mix of nonlinear inequality constraints, ...
0
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1answer
57 views

Is there general algorithms to solve such 3D cutting problems?

Suppose a cuboid $\mathbb{A}$ has $L$,$M$ and $N$ as its length, width and height respectively, where $L\ge{M}\ge{N}>0$; Now we want to cut $\mathbb{A}$ into smaller cuboids with length $x$, width ...
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0answers
26 views

Softly bounded linear regression

I am looking into implementing (in C++) a linear regression of few parameters (5-ish) to find moderate amount of data (2000-ish data points). Implementing least-square fit is straightforward; however, ...
0
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1answer
140 views

How to speed up fmincon in MATLAB when there are many variables? Alternatives to MATLAB optimization toolbox?

I need to solve an optimization problem with two nonlinear equality constraints. My function evaluation is very fast (less than a second) and I also provide fmincon ...
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0answers
24 views

Genetic Algorithm in linear cut optimization with reuse

As stated in the title i have a problem of linear cut optimization that i need to solve with a genetic algorithm. No problem if i have all the possible pieces to cut that are stically defined when ...
1
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1answer
88 views

Maximum translation distance between piecewise functions that satisfy a condition

The description: I have a number of similar piecewise functions, where $d$ is the translation distance lets assume this is the function (where a and b are known constants): $$f(x-d) = \left\{ ...
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0answers
44 views

how to compute Lagrangian multipliers for this case?

I have seen in the Pang book of data mining the following example: ...
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1answer
64 views

Constraint containing 'max' in linear program unnecessary?

The problem that I'm trying to solve is as follows. A server has at its disposal a pool of video encoders (each encoder has different settings and causes a different load on the server) that can be ...
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4answers
302 views

Levenberg-Marquardt - What is preferable (A + mu.I) or (A + mu.diag[A])?

The step size is computed by solving $$ (A + \mu I) h = -g $$ I could find in some literature that one can compute the step size by solving $$ (A + \mu \operatorname{diag}(A) ) h = -g $$ It is said ...
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1answer
38 views

Algorithms for searching in high-dimensional binary data spaces

Is there any algorithm that can learn/search efficiently the best sequence of 1's and 0's of length $n$ to fulfill certain performance? The search is performed in a high-dimensional binary data space. ...
2
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1answer
57 views

optimize vertices using a cost function on triangles

I want to optimize the vertex positions in a mesh, with a given cost function on the associated triangles. The paper gives a cost function, which evaluates to an real number by using a sum over the ...
0
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1answer
114 views

Doubt regarding stopping criterion for Newton method

I am solving an unconstrained convex optimization problem, which can easily have a million variables. I am trying to get a working system with a toy problem of around 200 variables. I am noticing that ...
0
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1answer
73 views

Unconstrained minimization of unbounded function with SciPy

It seems that scipy.minimize can find the minimum of an unbounded function. ...