# 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 ...

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### Quasiconvexity of a function on the positive orthant using rays

It is seen in Boyd's book on Convex Optimization book that to show a function $f:\mathbf{R}^n\rightarrow \mathbf{R}$ is quasiconvex, it is enough to show that $f$'s restriction to a line is ...
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### Proving equivalent optimization problems

Consider the problems $\min f(x) , x \in X$ and $\min g(x), x \in X$. two optimization problems are said to be equivalent if an optimal solution to one, is also optimal to another. I would like to ...
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### Convexity of n $4u^4x^{2.5}y^{-5}$ over $x>0, y >0$ and $u>0$

I am trying to find if the function $4u^4x^{2.5}y^{-5}$ is convex over $u>0, y>0$ and $x>0$. The thing which comes to my mind immediately is to check the positive semi-definiteness of the ...
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### School District Boundary Optimization--Interpreting the Objective Function

I’m looking for a little help on a new problem. I’m in a linear programming class and trying to work on a project exploring methods on nonlinear optimization and I came across the following question ...
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### Lagrange multiplier - maximum not on tangent contour

I am trying to validate how Lagrange multipliers work. Looking to maximize $f(x,y)=1-x^2$ along curve $x^2 + y^2 = 1$, the solutions are $f(0, -1) = f(0,1)=1$. However, according to Lagrange ...
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Assume $X$ to be a tall block-diagonal matrix where each block is a collumn vector. Assuming $X^+ = (X^H X)^{-1}X^H$ to be the pseudoinverse of the matrix $X$, find $X$ which maximizes y^H ( X X^+ ... 0answers 17 views ### NLP, Recatungular or Polar? Sine or No Sine? Let's say we have the following complex number, V: V=V_i+jV_j=V_m\angle{V_a} Which type of representation is better in an NLP (polar or rectangular)? The polar form leads to one nasty ... 0answers 29 views ### Can we solve this system of inequalities analytically? Let A be positive real number and k a positive integer. How to find the analytical solution of this system? Find the a_i \begin{align} \begin{cases} \displaystyle\sum_{i=1}^n\ln\left(1+a_i\... 1answer 62 views ### Why does f(x)=\frac{x^T Ax}{x^T x} always have a minimum value? f is defined for all x\in\mathbb{R^n}-\{0\} nd A is a symmetric matrix n \times n. I have to proof that f has a minimum f(x^*) and write a formula for x^* using the spectral ... 0answers 30 views ### A supremum problem Let a=\underset{\|u\|_c\leq 1, \|v\|_r\leq 1}{\sup}v^TY^Tu. If \lambda<a, \underset{u_m, v_m}{\sup}v_m^TY^Tu_m-\lambda\|u_m\|_c\|v_m\|_r=+\infty. While if \lambda > a, then \... 2answers 46 views ### Intersection of a power function with a line: how to compute? How to compute x fromq x^p = 1 - x where $x$ and $q$ are positive, while $p$ is a real number? When $p > 0$: it's two monotonic functions, one increasing and one decreasing, and having ...
How can I perform a regression onto data of that follows this shape: $$U(x):=\sum_{i=1}^N\, a_ix^ie^{-b_ix}$$ where the $a_i\in \mathbb{R}$ and the $b_i \in (0,\infty)$ ...