# Tagged Questions

A non-linear optimization problem includes an objective function (to be minimized or maximized) and some number of equality and/or inequality constraints where the objective or some of the constraints are non-linear. Use this tag for questions related to the theory of solving such problems or for ...

10 views

46 views

### Identify if optimization problem is convex or non-convex?

I have formulated optimization problem for building, where cost concerns with energy consumption and constraints are related to hardware limits and model of building. To solve this formulation, I need ...
30 views

### what should i replace the product of nonlinear variables with when linearizing

I have a product of two continuous variables in a constraint of an optimization problem. I want to linearize the product and use $$x_1 \cdot x_2 = y_1^2 - y_2^2$$ I followed the steps mentioned in ...
85 views

### Is this illustration of Gauss Newton wrong?

In this illustration the value of each iteration is the minimum of the 2nd derivative. But the Wikipedia page says: the advantage [of the Gauss–Newton algorithm] is second derivatives, which ...
15 views

### Preconditioning vs Re-orthogonalise for Non-Linear Conjugate Gradient Method

I am using CG to solve an optimisation problem. Since my cost function is ill-conditioned, I am looking at improving the performance either by using Preconditioning or Re-orthogonalisation, especially ...
26 views

### Using least squares regression to apply nonlinear function to time series data

If you have a nonlinear function (see example), can you use a least squares regression approach to fit it to time series data ? Is this approach also valid for n variables? How many time points are ...
31 views

75 views

### Maximize $2^{(-x)} + 2^{(-y)}$ subjected to certain conditions

I am reading through convex optimization and I came across this following problem: \begin{align*} \max \text{ } & 2^{-x}+2^{-y}\\ \text{s.t. } & \frac{1}{1+x}+\frac{1}{1+y}\leq b\\ & x\...
203 views

### Monotonic Function Optimization on Convex Constraint Region

So I have the following function, which I want to maximize: $$f(x_1,...,x_n) = \sum_{i=1}^n\alpha_i\sqrt{x_i}$$ (where all $\alpha_i$ are positive), subjected to the following equality and inequality ...
22 views

18 views

### How find the roots of non-convex function?

How to find a roots of non-convex function f(x)=0, where f is real scalar function of real scalar argument. What methods are exist for it? Or/And where I can to read about it?
33 views

26 views

### Examples of complex analysis useful in optimization?

Are there any examples of complex analysis applicable to mathematical optimization problems (preferably non-linear optimization)? I am wondering what advantages the use of complex numbers would have ...
43 views

### How to solve this KKT problem?

Given an optimization as follows: \begin{align} \text{minimize}\quad &c^Tx \\ \text{subject to}\quad &Ax = 0 \\ & \|x\|_2^2 \leq 1 \end{align} where $A \in \Re^{m\times n}$ is of ...
25 views

### What class of problem is a set of equations using inequalities and if-then-else?

Can you please identify what class of problem this is so that I can research algorithms for solving it please? Its a a set of linear equations and inequalities/constraints looking like this: ...
33 views

### Finding the gradient in least squares

In Linear squares optimization I have A=\begin{pmatrix} 1 & t_1 & t_1^2 & \cdots & t_1^k \\ 1 & t_2 & t_2^2 & \cdots & t_2^k \\ \vdots & \vdots& ...
How may I state the KKT conditions for minimize $f(x) = ax^2$ subject to $Ax \leq b$, $x$ unrestricted?