Computational Science Stack Exchange
Computational Science Stack Exchange

Questions tagged [optimization]

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

Questions on subjects like linear and nonlinear programming can also have this tag.

1004 questions
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Confusion about Armijo rule

I have this confusion about Armijo rule used in line search. I was reading back tracking line search but didn't get what this Armijo rule is all about. Can anyone elaborate what Armijo rule is? The wikipedia doesn't seem to explain well. Thanks
user34790
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17
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5 answers

Finding a global minimum of a smooth, bounded, non-convex 2D function that is costly to evaluate

I have a bounded non-convex 2-D function which I'd like to find the minimum of. The function is quite smooth. Evaluating it is costly. An acceptable error is about 3% of the function's domain in each axis. I tried running the implementation of the…
nojka_kruva
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14
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1 answer

Understanding the Wolfe Conditions for an Inexact line search

According to Nocedal & Wright's Book Numerical Optimization (2006), the Wolfe's conditions for an inexact line search are, for a descent direction $p$, Sufficient Decrease: $f(x+\alpha p)\le f(x)+c_1\alpha_k\nabla f(x)^T p$ Curvature Condition:…
Paul
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13
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3 answers

Optimize an unknown function which can be evaluated only?

Given an unknown function $f:\mathbb R^d \to \mathbb R$, we can evaluate its value at any point in its domain, but we don't have its expression. In other words, $f$ is like a black box to us. What is the name for the problem of finding the minimizer…
Tim
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13
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5 answers

Global maximization of expensive objective function

I am interested in globally maximizing a function of many ($\approx 30$) real parameters (a result of a complex simulation). However, the function in question is relatively expensive to evaluate, requiring about 2 days for each parameter set. I am…
AJK
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12
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3 answers

Confusion about compressed sensing problem

I read some references including this. I am kind of confused what optimization problem compressed sensing builds and tries to solve. Is it $$\begin{array}{ll} \text{minimize} & \|x\|_1\\ \text{subject to} &…
Tim
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11
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4 answers

Maximizing a convex function (minimizing a concave function) with a linear constraint

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

large dense low rank assignment problem

Is there a reasonably cheap method to solve the large, dense, low rank assignment problem $\max_\pi \sum_i A_{\pi i,i}$, where $\pi$ runs over all permutations.of $1:n$? Here $A$ is an $n\times n$ matrix of low rank $r$. Typical sizes would be …
Arnold Neumaier
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9
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2 answers

Optimization method that considers varying time cost of objective function for different parameters

I am working on improving the optimization process of some demographic modeling software so it can better fit demographic models to data. We'd like to decrease optimization time. The time it takes to evaluate our objective function varies a lot,…
nova
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9
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2 answers

Simultaneous maximization of two functions without available derivatives

I have two variables k and t as functions of two other variables p1 and p2. I also know their maximum values. I do not have any analytic expression for this. I want to find the values of k and t which are the closest to their maximum values. Is…
user1639
9
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3 answers

Is providing approximate gradients to a gradient based optimizer useless?

Is it pointless to use gradient based optimization algorithms if you can only provide a numerical gradient? If not, why provide a numerical gradient in the first place if it is trivial to perform finite differentiation for the optimization library…
professor bigglesworth
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9
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5 answers

How can I automate the process of optimizing the design of a physical object?

I'm trying to optimize a flow distributor in a tank such that the velocity and temperature distribution across any cross-section is relatively uniform. There are many parameters I can adjust to the maximum cross-sectional uniformity, such as the…
Paul
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9
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2 answers

Meaning of search methods and optimization methods

I was wondering what differences and relations are between "search methods" and "optimization methods"? Especially when solving an optimization problem? I emphasize the context of solving optimization problems, because I guess search methods are…
Tim
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7
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2 answers

Which is easier to solve, regularized minimization, or constrained minimization?

Following regularized minimization problem $$\min f(x) + \lambda g(x)$$ where $\lambda>0$, and following constrained minimization problem $$ \min f(x) $$ s.t. $$ g(x) \leq \epsilon $$ where $\epsilon>0$, can be converted to each other so that they…
Tim
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7
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2 answers

Confusion related to convex optimization

I have been reading about convex optimization. We have: minimize $f(x)$ s.t. $h(x) = 0$, $g(x) \le 0$, $x \in X$ It's Lagrangian dual is: maximize $\phi(\lambda,\mu)$ s.t. $\mu \ge 0$, where $\phi(\lambda,\mu) = \inf[f(x) + \lambda' h(x) + …
user34790
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