The nonlinear-optimization tag has no wiki summary.
2
votes
1answer
82 views
Non-linear 1st order difference equation
I have been trying to solve the following difference equation for some time now : $$u^3(n+1) = a - b\cdot u^2(n) + u^3(n), \qquad a \ne 0 \ne b$$
I have tried various substitutions, simplifications ...
0
votes
0answers
38 views
A minimization problem [migrated]
Define $$L(w,u)=\frac{1}{2}\|w-u\|^2+\beta \|\frac{w}{x}\|,~w,u\in R^n$$
where $$\frac{w}{x}=(\frac{w_1}{x_1},\dots, \frac{w_n}{x_n})$$
$$\|x\|=\sqrt{x_1^2+\cdots+x_n^2}$$
Given $u$, $x$ and $\beta$, ...
0
votes
0answers
27 views
An example of the Sequential Quadratic Programming (SQP) [migrated]
Given an objective function $f(x,y)=(x+6)^2+(y-10)^2$, we want to minimize the function $f$ under a constrained condition $xy-5\leq0$. Obviously it is a constrained optimization, a good algorithm to ...
0
votes
0answers
31 views
Optimization with differential inequality constraint
Consider the closed set $[t_1,t_2]⊂R_{>0}$ and $V(t):[t1,t2]→R_{>0}$ being a continuous and piecewise continuously differentiable function. We want to find a continuously differentiable function ...
0
votes
1answer
51 views
Nonconvex optimization problem
I have a nonconvex optimization problem. It is actually optimizing a linear objective function over a set of linear constraints and a set of nonlinear, non convex constraints.
Is this problem ...
0
votes
0answers
19 views
Minimum of a real-valued function of multiple variables
Suppose we are given two functions $$\phi(x) = \frac{\sigma^2}{2\mu^2} \left(1 - e^{-(2\mu/\sigma^2)x}\right) - \frac{x}{\mu}，x\in \mathbb R$$ and $$g_0(x) = \frac{\sigma^6}{4\mu^4} ...
1
vote
0answers
104 views
Recovering a partition from spectral properties of the graph Laplacian
Let $G$ be a weighted graph with vertices $V$. Let $W$ be its real-valued, non-negative, $|V|\times|V|$ adjacency/affinity matrix. Let $L = \mathrm{diag}(W\mathbf1)-W$ be the (unnormalized) graph ...
2
votes
1answer
118 views
Optimization problem - maximizing number of satisfied linear inequalities subject to a quadratic constraint
I am wondering what is known about optimization problems of the following type.
Our control x is a unit vector in $\mathbb{R}^n$. We are given a finite number of linear inequalities
$$Az≥b,$$
and we ...
0
votes
0answers
49 views
Big eigenvalues of a special stochastic matrix
Given a matrix $M$ of size $n\times n,$ we write its different eigenvalues by $x_1,x_2,\ldots,x_m$ with $m\leq n$ such that $|x_1|>|x_2|>|x_3|>\cdots|x_m|,$ and call $x_2\doteq ...
2
votes
1answer
49 views
Conjugate gradient algorithm where first search direction is not equal to residual
In usual formulation of conjugate gradient algorithm initial search direction is taken to be the residual (so residual and search direction spans Krylov subspace). However, in cases where inexact ...
2
votes
0answers
92 views
Quadratic optimization with parameter in constraint
Disclaimer: I posted the same question on math.stackexchange. However, the FAQ suggests to post research-level questions in this forum.
Question: Given a function $q: \mathbb R^{N\times N}\mapsto ...
3
votes
3answers
134 views
Constraint optimization problem for any dimensionality $n>1$.
I am going to post a particular example for the sake of clarity.
One needs to maximize a real function
$F = a_1a_2 + a_2a_3 + \cdots + a_{n -
> 1}a_n + a_na_1;$
with active ...
3
votes
1answer
366 views
The average number of people that can sit on a bench of a given length.
Let me explain what I mean:
The width of the average person varies, perhaps with a normal distribution.
Given a specific variance, how many people (on average) can sit side-by-side on a bench of a ...
2
votes
1answer
122 views
Maximizing supermodular functions
I have a real supermodular objective function which I want to maximize with constraint. The constraint is on the size, like |A|=k .
I am wondering if anyone can give me more information about a ...
0
votes
0answers
63 views
Optimal instance of quadratically constrained program
Consider the following optimization problem. Let $n, m \in \mathbb N$ and $0 < p_1 \leq \ldots \leq p_n ~ (p_i \in \mathbb R)$ be constant. The feasible region is described by a partition $T_1, ...
