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

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38 views

Oscillating convergence in my Resilient BackPropagation (RPROP) implementation

I have implemented in matlab a neural network that uses rprop's algorithm to update its weights. Strangely the error on the training set does not converge to a local minimum, but oscillates. Here is ...
5
votes
1answer
51 views

Can Variational Inequalities handle non-symmetric matrices?

I am trying to enforce the discrete maximum principle (i.e., ensuring non-negative concentrations) for diffusion-type problems that have an anisotropic diffusivity tensor (e.g., tensor dispersion from ...
1
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1answer
60 views

How to formulate variance minimization as a mixed integer quadratic program

I have a mixed integer quadratic problem and my objective function is as follows $$\arg \min \operatorname{Var}(f(x),g(x)) + \operatorname{Var}(c(x),d(x)) + \cdots$$ where $f$, $g$, $c$ $d$ are ...
0
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0answers
40 views

Which optimization toolbox is suitable for this type of problem

I have a mixed integer (quadratic/linear) optimization problem with about 3000 variables in a form which I can't extract the coefficient vectores. However MILP solver in Matlab requires the f input ...
0
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1answer
39 views

Can Variance be replaced by absolute value in this optimization problem

Initially I modeled my objective function as $$\arg \min \operatorname{Var}(f(x),g(x)) + \operatorname{Var}(c(x),d(x)) + \cdots$$ where $f$, $g$, $c$, $x$ are linear functions. To be able to solve ...
3
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1answer
38 views

Semidefinite Programming Using CVX in Matlab

I have the following optimization problem $$\begin{align} &\min_{ X_{1}, \dots,X_{k} } \max_{ \theta, \phi } \left|P_{d}(\theta,\phi) - \sum_{k=1}^K ...
1
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1answer
56 views

Profiling optimized C code using gprof

I have a simple C code with many function calls, which I profiled using gprof. ...
0
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1answer
50 views

adjoint method package for ODE(PDE)-constrained optimization

I have this type of question (ODE-constrained optimization) to solve: $g(x,p)=0$ is the simulation, where $x$ is state variable and $p$ is parameters aimed to optimize; $f(x)$ is the objective ...
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0answers
34 views

Manipulating/Extracting Data and Developing Methods - Language Choice [closed]

As a general programming enthusiast and aspiring Bioinformatician student I have an intermediate understanding of computing (languages) as well as Java, and to a lesser extent C++. Having knowledge in ...
1
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2answers
76 views

Building minimization optimization problem for 2nd-order elliptic PDE

I am solving elliptic PDE problem, for which, Euler scheme looks as following: $$ \nabla [\gamma ( |\nabla u|^2) \nabla u] = 0,$$ where $$\gamma(|\nabla u|^2) = (1 + |\nabla u|^2)^{-1/2}. $$ I am ...
4
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1answer
46 views

Optimal partitioning of a graph

Consider a planar graph, where each node is associated with a weight. I would like to partition the graph such that the sum of the node weights in each group satisfy a minimum requirement. However, I ...
0
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0answers
24 views

Optimization of a molecular dynamics coarse grain model

I am trying to optimize a model I develop for molecular simulation, however, I have zero experience in optimization and I need some guidelines in approaching the solution. I basically do not know ...
1
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1answer
63 views

Linear vs Non Linear inverse problems: Does non-linearity help?

This is not a typical question with a deterministic answer. If this is not the right place, feel free to close it. For the past one year I have been working on various kinds of inverse problem. Most ...
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0answers
39 views

A better way to compute a double integral involving a infinite series?

Let $D_{\nu}(.)$ is the parabolic cylinder function (http://mathworld.wolfram.com/ParabolicCylinderFunction.html) And $\Gamma(.)$ is the Gamma function. Define ...
1
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0answers
32 views

Optimization with matrix exponential constraint

Suppose I'm optimizing for an unknown $x\in\mathbb{R}^k.$ I have a linear operator $A(\cdot)$ that maps $x$ to an $n\times n$ symmetric matrix, i.e., $A:\mathbb{R}^k\rightarrow\mathbb{R}^{n\times ...
1
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1answer
49 views

Algorithms for one-to-many assignment problem

I'm looking for a computationally efficient algorithm for solving the following type of assignment problem: I have two sets of points. Set A has N points and set B has M points. I'd like to establish ...
2
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0answers
39 views

Inverted value is not consistent with expectation

We have a group of observations $$y = f(x_1, x_2, x_3) \enspace .$$ We have also a forward model $y = f(x_1, x_2)$. The forward model does not include $x_3$ because $x_3$ might include dozens of ...
2
votes
1answer
70 views

How can I solve a nonlinear optimization problem where constraint contains exponential term?

I have the optimization problem as below: $$\begin{align} &\text{maximize } \sum_{k=1}^{M} \alpha_k {R}_k\\ &\text{subject to: } \exp \left[ - (2^{{R}_k } -1) \left(\frac{\tilde{Z} g_{k} ...
0
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0answers
41 views

Solving an LP greedily

I have the following LP: $$ \begin{array}{ll} \text{Minimize} & \sum_{j=1}^n x_j \\ \text{Subject to} & \sum_{j=1}^n a_{ij} x_j \geq b_i,~~~i\in\{1,\ldots,M\} \\ & 0 \leq ...
0
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0answers
20 views

“Tunneling” optimization algorithm in Matlab

I was wondering if someone has implemented the "Tunneling algorithm" for the global minimization of a single variable function in Matlab. I am hoping to implement it on $[B, A - \lambda I]$. Where ...
0
votes
1answer
75 views

what is the upper bound of $\max \mathbf{w}^T\mathbf{x}_i$

I need to find an equation for the upper bound of $\max \mathbf{w}^T\mathbf{x}_i, \; i=1, \dots N$. where $\mathbf{w}$ and $\mathbf{x}_i$ are two vectors. I need to find a function $f$ which holds ...
3
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0answers
57 views

Maximizing slow multi-parameter function

What's the best method to maximize the value of slow multivariate function? Here is what I know about the function: Number of parameters is ~ 10. It takes considerable amount of time to compute the ...
8
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0answers
139 views

scale invariance for line-search and trust region algorithms

In Nocedal & Wright's book on Numerical Optimization, there is a statement in section 2.2 (page 27), "Generally speaking, it is easier to preserve scale invariance for line search algorithms than ...
0
votes
1answer
31 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 ...
1
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1answer
61 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
votes
3answers
112 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 ...
3
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0answers
31 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
115 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: ...
1
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0answers
28 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}} ...
0
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0answers
52 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 ...
5
votes
2answers
128 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
votes
1answer
112 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
votes
1answer
85 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 ...
0
votes
1answer
35 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
57 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: ...
1
vote
2answers
60 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 ...
0
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0answers
32 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 ...
1
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2answers
129 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
votes
2answers
175 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 ...
4
votes
1answer
76 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
votes
2answers
80 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
34 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
votes
2answers
69 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 ...
0
votes
1answer
64 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
votes
1answer
50 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
votes
2answers
121 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 ...
1
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1answer
25 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 $C_1$ ...
1
vote
1answer
44 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 ...
1
vote
2answers
128 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 ...