# Questions tagged [nonlinear-optimization]

Nonlinear objectives, nonlinear constraints, non-convex objective, non-convex feasible region.

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### How to derive Slime Mould Equations

As shown in https://en.wikiversity.org/wiki/Slime_Mould_Algorithm, we have the Slime Mould equations for Approach food and Wrap food. I do not know how to derive these equations. Please help me or ...
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### Numerical scheme for convex optimization

Given $(e_n)_{-N\le n\le N}\in\mathbb R^{2N+1}$ and $-1<x<1$, solve \begin{eqnarray} &&\max_{(q_n)_{-N\le n\le N}\in\mathbb R^{2N+1}_+}~ \sum_{n=-N}^N (e_n-\log(q_n))q_n \\ \mbox{s.t.} &...
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### Was a quotient of two norms considered as a constraint to a convex optimization problem before?

I want to solve the optimization problem $$\text{minimize }g(x) \quad \text{subject to} \quad \Vert x\Vert_{\infty}/\Vert x\Vert_{2} \le s$$ for $x\in\mathbb{R}^d$ and $s\in(0,\infty)$. The function ...
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### Breaking up an infinite-dimensional optimization problem into a sequence of finite-dimensional problems

My question is a bit vague. I have an infinite-dimensional convex optimization problem and I can solve constrained versions of the problem by restricting the domain of the objective function to a ...
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### What is Young measure?

I read about Young measures from the book, Weak convergence methods for nonlinear partial differential equations by L.C. Evans. He introduces the concept by the following theorem: Theorem. Assume ...
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### Variant of Parthasarathy's minimax theorem

Does there exist a variant of Parthasarathy's minimax theorem  that relaxes the assumption that the spaces $X$ and $Y$ are $[0,1]$?  https://en.wikipedia.org/wiki/Parthasarathy%27s_theorem
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### optimization to find the maximum of sum of sigmoids with some constraints

I am having a problem of maximizing a sum of sigmoid functions over different time instants with some constraints. Considering the standard sigmoid function $f(x)=\frac{1}{1+e^{-\alpha x}}$ and it's ...
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### Looking for a very particular kind of non-convex functions

I want some examples (hopefully parametric families!) of non-convex functions which satisfy the following properties simultaneously, It should be at least twice differentiable. It should have a ...
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### What to call a function that is negative on a set

Let $Y$ be a nonempty region in $\mathbb{R}^n$. I am designing an algorithm which given a point $x_0$ outside $Y$ in a finite number of steps lead to a point $x_n∈ Y$. The way I do it is that I have a ...
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### How to solve a system of nonlinear equation, with y known and x or its coefficients unknown? [closed]

While solving a complex problem I have ended up with this simplified problem: There are eight straight lines in the plane. They are notated as follows: \begin{gather} \tag{1} \label{1} y=k_1 x+b_1\\ y=...
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### Minimizing the largest eigenvalue of matrix product

Let $A\in\mathbb{C}^{m\times n}$, $B\in\mathbb{C}^{n\times k}$, $C\in\mathbb{C}^{k\times m}$ be given complex matrices. The objective of the optimization problem is \begin{equation} \mathop {\arg \min ...