Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [numerical-optimization]

Numerical methods for continuous optimization.

Numerical Optimization is one of the central techniques in Machine Learning. For many problems it is hard to figure out the best solution directly, but it is relatively easy to set up a loss function that measures how good a solution is - and then minimize the parameters of that function to find the solution.

Learn more about solving numerical optimization problems in this pdf.

Sources: http://www.benfrederickson.com/numerical-optimization/

1526 questions
0
votes
0 answers

Numerical optimisation of time series / balance sheet

Have an excel financial model, that pretty much is a time series of assets and liabilities. I would like to know what the optimal liability structure / mix is, subject to multiple balance sheet constraints. My objective function is to minimise…
legendary kaya
  • 1
0
votes
0 answers

What is a reasonable alphaMin in line-search optimization?

Ipopt uses alphaMin=1.0e-8, i.e., IPOPT will give up the backtracking line-search procedure whenever alpha falls below alphaMin. Now I'd like some parameter that is less error-prone to scaling. I thought of $$ \alpha_{min} = 10^{-6} \cdot \frac{…
MustafaBientivi
  • 3
0
votes
0 answers

Maximum value of addition of some elements of a set

A. If I have a set of natural numbers $\{x_1,x_2, \dots, x_n\}$. How can I maximize a sum of numbers with the following rules: Every number of the summands is at most the maximum value of their corresponding number of the set. If the number doesn't…
DFKMR
  • 1
0
votes
0 answers

Trust region subproblem

I'm triying to replicate this paper: https://iopscience.iop.org/article/10.1088/1742-6596/1818/1/012022/pdf But I don't know how implement this part: Find $d_{k}$ such that $$\min q_{k}(d) \quad \text{such that} \quad ||d|| \le \quad…
Marinela
  • 569
0
votes
0 answers

Numerically minimize a function

question screenshot I am very bad at maths in general, so I dont even know which topic this question falls into. Got this from a mathemtatics exam, and I would like to know where can I get some example solutions related to this question. I…
AgUn
  • 1
0
votes
1 answer

Initial feasible solution for barrier method

From this example page 9 It said set initial feasible solution at 2 here's barrier function: $$T(x)=\frac{100}{x}+\frac{1}{r}(\frac{-1}{x-5})$$ after derivative: $$\frac{\delta T}{\delta x}=\frac{1}{r(x-5)^2}-\frac{100}{x^2}$$ we show x in terms of…
Linear Algebra fans
  • 63
0
votes
1 answer

Optimization problem: Computing the gradient

I need help with the following exercise: Solve $\min_{x\in\mathbb{R}^d} f(x)$, where $f:\mathbb{R}^d\to\mathbb{R}$. We define the inner product $(v,w)_A:= v^TAw$, induced by a positive definite and symmetric matrix $A\in\mathbb{R}^{d \times…
Joseph
  • 65
0
votes
1 answer

Best approximantion of sin(x) with a constant function

I am trying to understand how to show that the best approximation of $\sin(x)$ over $[0,\pi]$ and polynomial of degree $n=0$ (so a constant $c$) by using the maximum norm, i.e $\min_{c} \lVert \sin(x) - c\rVert_\infty$ is with $c=1/2$. Visually it…
R. Carlos
  • 101
0
votes
0 answers

derivative-free optimization

I'm using the Nelder-Mead algorithm for a project. Is there any way I can guarantee that the method will find find the absolute minimum of my function if my function has multiple local minima? Is the method highly dependent on my initial…
D.B.
  • 2,339
  • 8
  • 11
0
votes
1 answer

Solving DIMACS 7 problems using MOSEK and YALMIP

I'm trying to test the MOSEK solver in the YALMIP MATLAB environment to try and solve a DIMACS 7 problem, but am having some issues. In particular, I'm trying to solve the "sched_50_50_orig" problem given near the bottom of the following link:…
InquisitiveInquirer
  • 221
0
votes
1 answer

ProxASAGA: compute and use the support of $\Delta f$

Here is the situation: I am trying to implement an algorithm called ProxASAGA. We have a set of functions $f_i: R^n \rightarrow R$ and we are trying to minimize their mean $$ \frac{1}{n}\sum_{i=1}^nf_i(x). $$ On every iteration, there are the…
Arthur Feldman
  • 13
  • 6
0
votes
1 answer

what does it mean to be correct to within an order of magnitude?

Nocedal and Wright in their book Numerical Optimization have this: ... The four constants differ greatly in magnitude, since the reacions take place at vastly different speeds. Suppose we have the following rough estimates for the final values of…
O. Altun
  • 365
0
votes
1 answer

Given three numbers determine the fourth

This is eluding me. I have four different databases with the following row/record counts (specified in the titles) with corresponding total database sizes. I need to determine what the database sizes will be when there are 50 million records.…
D-Klotz
  • 103
0
votes
1 answer

Steepest descent method and how to find the weighting factor

I am trying to understand the numerical method of finding a minimum, the steepest descent method. \begin{equation} x_1 = x_0 - \alpha \frac{df}{dx} \end{equation} I understand the idea behind it and how to set up the equation, but I do not get: How…
Nenunathel
  • 295
0
votes
1 answer

Comparison of augmented and standard Lagrangian methods

I understand that augmented Lagrangian methods, add penalty terms to standard Lagrangian method. The question is what is wrong with original standard Lagrangian method, that made people add a quadratic penalty term. This is not a deep question, I…
user25004
  • 3,586
  • 2
  • 33
  • 61
1
2
3