# Questions tagged [nonlinear-optimization]

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 trying to solve particular problems.

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### How to reformulate negative power of posynomial as a geometric programming constraint?

Currently, I am working as a network optimization engineer. From what I see, most of my optimization task can be fulfil effectively by using Geometric Programming (GP). However, I am running into a ...
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### Using Block Coordinate Descent for Convex Optimization with Quadratic Constraints

In solving the optimization problem $$min _{X, Y} f(X, Y)$$ $$\text { s.t. } \operatorname{tr}\left(X X^T\right)+\operatorname{tr}\left(Y Y^T\right) \leq P$$ , where both $f_X​(Y)$ and $f_Y​(X)$ are ...
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### Sequential projection onto circumferences

Let $S = (s_1, \dots, s_n) \subset \mathbb{R}^{n \times m}$ be a sequence of euclidean spheres, where $s_k = \{ x : \| c_k - x \|^2_2 \leqslant r_k^2\} \subset \mathbb{R}^m$ is the sphere $s_k \in S$ ...
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A version of this question was asked a couple of years ago here, but I am still not clear on why this is not used more widely (or seemingly at all). Problem statement: Suppose you have some ...
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### Linear optimization objective with little-o notation in constraint

I am trying to solve a problem related to matrix decomposition. In essence, it is a maximin problem of the following form $$\max_x \min_{j} \left[f_{j=1}^{(n)}(x),f_{j=2}^{(n)}(x),...\right]$$ where ...
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### Unimodality of multivariable quadratic functions

Are multivariable quadratic functions necessarily unimodal, so local optimum is always the global optimum? When the Hessian is indefinite then can we conclude the quadratic function is either ...
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### Concave maximization over $d$-dimensional simplex.

Can either an analytic solution or the dual be characterized for the following concave maximization: $v:= \underset{w \in \Delta_d}{\max} \sum^{d}_{i=1}\frac{1}{\sqrt{1+b_i/w_i}}$ where $\Delta_d$ ...
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### SOCP and polynomial time constraints

Given a multi-variable function $f$ to minimize subject to some constraints, I am confused after reading few papers and the Wikipedia entry about SOCP(second order cone programming). I already know ...
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### What is so interesting about the Armijo-Rule or the Wolfe-Conditions for choosing the right step size?

Right now I am taking a course on nonlinear optimization where we currently talk about step size rules(Armijo-Rule and Wolfe-Conditions). I also had a course 1 year ago about statistical machine ...
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### What is so interesting about the lagrange-newton method?

I have taken a course on nonlinear optimization. There we discussed penalty and barrier methods for nonlinear optimization. In the end my lecturer gave a short conceptual idea of SQP by introducing ...
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### Non-linear parameter optimization using Python

I have a model that generates the curve represented by the red squares the data represented by the black circles. The model curve (red squares) depends on some parameters to fitting. Is there any ...