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

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24 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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0answers
10 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
19 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
94 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 ...
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1answer
50 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 ...
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1answer
45 views

use line segments to approximate one function

I need to use line segments to approximate one 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
36 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
33 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 ...
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1answer
53 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
33 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
97 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
64 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
37 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, ...
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1answer
51 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
25 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, ...
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1answer
80 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 ...
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1answer
84 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
42 views

how to compute Lagrangian multipliers for this case?

I have seen in the Pang book of data mining the following example: ...
2
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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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2answers
217 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
37 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
56 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 ...
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1answer
107 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 ...
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1answer
67 views

Unconstrained minimization of unbounded function with SciPy

It seems that scipy.minimize can find the minimum of an unbounded function. ...
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0answers
41 views

stochastic optimization with unknown distribution

I have a stochastic optimization problem in which I have expectation in constraints. we do not have any any information about distribution function of the random variable a prior. I know in cases you ...
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2answers
133 views

Nearest positive semidefinite matrix to a symmetric matrix in the spectral norm

So I have a symmetric matrix $A$ and I would like to solve the optimization problem: $$\text{Minimize}\;\; ||A-S||_2$$ $$\hspace{-5mm}\text{Subject to}\;\; S\geq0$$ $A$ is given and $S$ is the ...
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2answers
60 views

Optimization: Providing gradients by autodifferentiation e.g PyAutoDiff

What is the difference (in terms of e.g robustness and speed) between proving a gradient obtained by an AD package (like PyAutoDiff) and let the solver (e.g BSGS) calculate the gradient ? It seems so ...
2
votes
1answer
106 views

optimization (using python) how to find the most suitable solver?

I have a fitting routine set up. It works, but pretty slow. I was wondering if there is a better method to use. I checked my (forward) code against some literature data and at least I do have no bugs ...
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0answers
32 views

Dynamic programming as final value problem?

I refer to the note "Stochastic systems" by Geering, Dondi, Herzog, Keel (freely available as a pdf ); We consider a stochastic optimal control problem, i.e. given a dynamical system with state ...
2
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1answer
73 views

Generalized linear-fractional program [closed]

Given the generalized linear-fractional program: $$\text{Minimize}\;\; \max_{i}\Big|\frac{c_i^Tx+d_i}{e_i^Tx+f_i}\Big|$$ $$\hspace{-5mm}\text{Subject to}\;\; e_i^Tx+f_i>0$$ I convert this into the ...
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0answers
72 views

Help with the definition of constraints for a joint optimization problem

A trajectory is piecewise defined by the following polynomial form: $$ f(t) = a + bt+ct^{2}+dt^{3}+et^{4}+ft^{5}+gt^{6}+ht^{7}+it^{8}+jt^{9} $$ for every single segment composing the trajectory (the ...
2
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2answers
107 views

Find $\min x^TAy$ subject to $1^Tx=1^Ty=1,x\ge 0,y\ge 0$

In the following problem, $A$ is a given $\mathbb{R}^{m\times n}$ matrix: \begin{align} \mbox{minimize}\quad & x^TAy \\ \mbox{subject to}\quad & 1^Tx=1^Ty=1, \\ & x\ge 0,y\ge 0. ...
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1answer
146 views

Converting quadratic constraint to linear matrix inequality

So I have the quadratic programming problem: (x is the variable) $$\text{Minimize}\;\; x^T\Sigma x$$ $$\hspace{15mm}\text{Subject to}\;\; p^Tx = \frac{1}{n}p^T\boldsymbol{1}$$ ...
2
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1answer
61 views

Piecewise linear optimization with resource allocation constraints

I have this problem: \begin{align} \min_{\mathbf{w}} & \sum_{i=1}^N c_i P_i(w_i)\\ s.t & \notag\\ & \sum_{i =1 }^N w_i = w \\ & 0 \leq w_i \leq w_{max},~~\forall i \in 1, ..., N ...
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0answers
71 views

Search Direction in Conjugate Gradient

Could you help me with a Conjugate Gradient question? In using CG to solve Ax=b, why is the search direction $p_{k+1}$ in CG chosen as a linear combination of the residual $r_k$ and previous direction ...
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0answers
66 views

Reference request for numerical variational method

I have a variational problem where the unknown function is a periodic path $\gamma:[0,1)\to\mathbb{R}^2$, and the functional is $$ \int_0^1\left( \tfrac12\|\dot\gamma(s)\|^2 + ...
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0answers
77 views

Using the Nelder-Mead algorithm to find a maximum

In the Nelder-Mead algorithm, the simplex looks for the minimum of the function. If I multiply all the function values times -1, would I trick the simplex into searching for the maximum?
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3answers
151 views

optimization non linear problem with java code

Is there some packages in java that can be included to eclipse in order to solve a non linear problem? I have used ipopt but when running, there is a notification which say "NOTE: You are using Ipopt ...
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1answer
85 views

Minimization of The Blind Deconvolution Functional

I want to minimize the functional of teh Blind Deconvolution model as given in: Total Variation Blind Deconvolution by Chan and Wong. Their model is given by: $$ z = h \ast u + \eta $$ Where $ \ast ...
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0answers
145 views

How to solve this problem using Particle Swarm Optimization?

I'm currently revising my optimization algorithm for a specific part of a problem. I have trouble in wrapping my head around a new approach and my mind is having this tunnel-vision of ideas. I could ...
0
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1answer
68 views

Largest Cylinder inside Polyhedron

Imagine you have a piece of wood and from that piece you want to get the largest cylinder possible. How do you determine the position and orientation of the cylinders axis, to maximize its radius? ...
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0answers
84 views

Solving 10000, Non-Linear, Simultaneous Equations

Could anyone let me know if there is any optimization solver that I can use to solve about 10,000 simultaneous equations (most of which are non-linear) using Python? Please also advise if it is ...
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0answers
55 views

Coding a convex problem in CVX

I am new to CVX and am trying to simulate this convex problem I found in a paper. $$\min_{\gamma,\mathbf{mu},\mathbf{G},\mathbf{\Omega},t} \text{Tr}(\mathbf{G}\mathbf{C}\mathbf{G}^H)+t \\ s.t. ...
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2answers
61 views

MILP formulation and optimization

For $i=1, \dotsc, K$, we have $n_i$ ordered real numbers: $$ x_i(1) \leq x_i(2) \leq \dotsc \leq x_i(n_i) $$ I want to solve the following optimization problem: \begin{align} \mathrm{maximize} \; ...
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1answer
75 views

Global optimization methods in computational chemistry

I'm looking for a current and comprehensive overview (like a review article) of global optimization methods and their application in computational chemistry. Mostly I'm interested in geometry ...
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0answers
88 views

Optimizing rank computation for very large sparse matrices

I have a sparse matrix such as ...
1
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1answer
68 views

Discrete optimization on a cartesian product with component-wise increasing objective function

The set-up is the following: We have $K$ finite sets of real numbers, i.e. sets $G_i, i=1 \dotsc, K$ and $|G_i| = n_i < \infty$. Furthermore, assume that we have a function $$ h: \mathbb R^K ...
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1answer
209 views

Disciplined convex programming error: Only scalar quadratic forms can be specified in MATLAB's CVX

I want to minimize $$W\, \text{tr}\left([A-Y_{pie}][A-Y_{pie}]^T\right) + \lambda\Vert A\Vert\, \enspace ,$$ however, I encounter the following problem: ...