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Computer Science Stack Exchange

Questions tagged [optimization]

Questions about problems that entail selecting the best element from some set of available alternatives, and methods to solve them.

1828 questions
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Choosing a subset to maximize the minimum distance between points

I have a set of points $C$, and I have the distance between each point $D(P_i,P_j)$. These distances are euclidean but the points are actually in a feature space. From the $C$ points I want to choose a subset of $n$ points. Call this subset $s$. I…
user1389800
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10
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Maximizing a convex function with a linear constraint

$$\text{maximize } f(\mathbf{x}) \quad\text{subject to } \mathbf{Ax} = \mathbf{b}$$ where $$f(\mathbf{x}) = \sum_{i=1}^N\sqrt{1+\frac{x_i^4}{\left(\sum_{i=1}^{N}x_i^2\right)^2}},$$ $\mathbf{x} = [x_1,x_2,...,x_N]^T \in \mathbb{R}^{N\times 1}$ and…
Sooraj
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9
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1 answer

BFGS vs L-BFGS -- how different are they really?

I am trying to implement an optimization procedure in Python using BFGS and L-BFGS in Python, and I am getting surprisingly different results in the two cases. L-BFGS converges to the proper minimum super fast, whereas BFGS converges very slowly,…
ap21
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6
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3 answers

Interpolation Optimization Problem

I will try to give the motivation behind this problem and later the math formality. Given a grayscale image (1 Channel - M by N Matrix). Someone marks some pixels as anchors. Now, you need to interpolate the other pixels (Which are not anchors) by…
Royi
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5
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2 answers

Global Optimization of a well-defined function with gradient information

I try to minimize the function $$ f(x_1, …x_n)=\sum\limits_{i}^n-a_i\cos(4(x_i-b_i)) +\sum\limits_{ij}^\text{edge}- \cos(4(x_i-x_j)), \quad x_i,b_i\in (-\pi, \pi)$$ where $\sum\limits_{ij}^{edge}$ only sums over predefined edges (the edges are…
whitegreen
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4
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1 answer

Can one have a condition like this in semidefinite programming?

Is it possible to have the following condition in a semidefinite programming as a constraint? $ M= \left[ {\begin{array}{cc} a & \sqrt{u} \\ \sqrt{u} & b \\ \end{array} } \right] …
Star
4
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1 answer

How can I do an optimization problem that involves finding a sequence?

The problem I am trying to solve is to find the fastest way to produce an total amount of something. There are several different producers that each have a different production and cost (based on the number of the item that is already owned) which…
Reed Oei
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3
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1 answer

Buying as many items for as much money

I cant find a way to implement a certain solution. Let me flesh out the problem. Somebody gives you X amount of money and sends you to the shop to buy Y amount of items. You must spend as much money as you can and buy as many items as you can. You…
MateuszC
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3
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Defining the goal function in an optimization problem

I have an optimization problem. There are a few quantities, call them $a, b, c$, that describe how good a solution is. However, they all have different priority, from highest to lowest: $a, b, c$. The goal is to minimize the values of $a, b, c$. The…
user5539357
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3
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Gauss-Newton algorithm implementation

I am trying to implement a Gauss-Newton algorithm for non-linear optimisation. Unfortunately despite searching through the library and the internet I can't figure out quite how to use it in my case. As such I am hoping that I have come to the right…
Janet the Physicist
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Given an antisymmetric matrix, how do I find a set of rows that maximizes function?

Let $P$ be an $m \times m$ antisymmetric matrix of the form: $$ \begin{bmatrix} 0 & p_{1,2} & ... & p_{1,m} \\ -p_{1,2} & 0 & ... & p_{2,m} \\ \vdots & \vdots & \ddots & \vdots \\ -p_{1,m} & -p_{2,m} & \dots & 0 \\ \end{bmatrix}$$ with $p_{i,j} \in…
hennyk
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3
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Why would this Semidefinite Program be Dual Infeasible?

My semidefinite program amounts to two constraints, $L_1 = 0$ and $L_2 = 0$ where $L_i$ are linear functions of my variables $x_{ij}$ with the additional constraint that the $x_{ij}$ matrix is positive semidefinite. I see no way that this program…
Mark
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3
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Transform a set of points to have a minimum distance between them

Assume I have a set of $N$ ordered points, $X$. I would like to find the set of $N$ points, $Y$, where the distance between $X$ and $Y$ $(d = \sum_{i=0}^{N-1} |X_i - Y_i| )$ is minimized but there is a minimum distance between points of $M$…
Raphael Erik Hviding
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What is an appropriate global optimization technique for a noisy and expensive function?

I have a function which takes 22 real-valued parameters as input that returns a real value. The function is reasonably fast for low return values (ms/seconds/minutes), but takes much longer (minutes/hours) to compute for high/optimal values. The…
bobbaluba
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3
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Find the minimal subset of rows of some matrix such that the sum of each column over this rows exceeds some threshold

Let $A$ be a an $n\times m$ real valued matrix. The problem is to find the minimal subset $I$ of rows (if there is any) such that the sum of each column $j$ over the corresponding rows exceeds some threshold $t_j$, i.e. $\sum_{i\in I}A[i,j]>t_j$ for…
a.p
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