# Questions tagged [non-convex]

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### Cost function of neural networks can be non-convex, then why do we use it?

I saw a thread here (Cost function of neural network is non-convex?). After I read this, I am really confused. I am wondering that if the cost function is not convex, and we do backpropagation, then ...
1 vote
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### How do linear constraints affect the convexity of my OLS-like optimisation problem?

I would like to augment a linear regression (so a convex OLS problem) with some additional constraints on the coefficients to match the subject I'm working on. Having $x\in \mathbb{R}^n$, the solution ...
10 views

### Convergence analysis for federated learning using DNN model

In convergence analysis of federated learning (FL), usually, we have an assumption that the loss function is strongly convex. However, when the loss function model is non-convex, e.g., using DNN, I ...
737 views

### Are there any "convex neural networks"?

Are there any neural network training procedure that involves solving a convex problem? Note that I am referring more to MLPs, instead of (multi-class) logistic regression which is a neural network ...
78 views

### Is this objective function convex? [closed]

Given that $F(x)$ is the cumulative distribution function (CDF) of continuous random variable $X$, is $$\frac{\int_0^\infty 1-F(x) dx}{\int_{-\infty}^0 F(x) dx}$$ convex? or is it non-convex/concave? ...
102 views

### Does coordinate wise convex function can be optimized more effectively?

I'm currently working on a non-convex function. It's basically a maximum likelihood problem so I'm trying to optimize this function. I know that non-convex optimization frequently reaches local optima ...
1 vote
122 views

### Convergence under large set of learning rates

What is the interpretation of a stochastic optimization problem where a gradient descent algorithm is converging under a wide range of learning rate schedules (including ones with quite large initial ...
1 vote
129 views

### How to minimize the sum of Frobenius norm and Nuclear norm

I have to minimize an objective function of the the form : $||X_{s} - Y_{s}D_{s}||_{F}^{2} + ||D_{s}||_{F}^{2} + ||D_{s}||_{*}^{2}$ where $||.||_{F}$ denotes the Frobenius norm and $||.||_{*}$ ...
391 views

### Why are K-means and GMM (Gaussian Mixture Models) not suitable for discovering clusters with non-convexs shapes?

I have seen that mainly here and from a lot of resources that K-means and Hello all! Gaussian mixtures are not suitable for detecting clusters with non-convex shapes. I know that because both ...
46 views

### If $\ell_0$ regularization can be done via the proximal operator, why are people still using LASSO?

I have just learned that a general framework in constrained optimization is called "proximal gradient optimization". It is interesting that the $\ell_0$ "norm" is also associated with a proximal ...
677 views

### Solving constrained optimization problems with Adam

The adam algorithm has been very successful for solving non-convex optimization problems that appear in deep learning. Are there ways to extend adam to solve constrained optimization problems? Among ...
41 views

### How to solve a non-convex with equality constraint optimization problem?

I have a non-convex optimization problem with equality constraint, I can derive the KKT conditions, but it seems just one of the KKT conditions is valid. Could you please give some advice on how to ...
483 views

### Is error function always assumed and convex?

While updating weights of the neural network, most of the algorithms use convex optimisation because of the reason that error is a convex function. My doubt is that whether the convex-ness of error ...
1 vote
357 views

### How to optimize ratiometric loss function with variance term in it?

I'm training a neural network (or any ML model with non-convex gradient-based optimization) to predict a continuous outcome variable. Currently, I use the mean squared error loss function, i.e., if $y$...
253 views

### Optimization textbooks for statistics and data analytics

Any statistical analysis, machine learning or data science involves some sort of optimization at the end of the day. I'm looking for good linear and nonlinear optimization textbooks for self ...
1 vote
39 views

### Minimal requirement for reaching a feasible solution in non-convex constrained gradient descent

The problem is as follows: $\max_x f(x) \enspace , \enspace \text{s.t.} \enspace g(x) \leq \alpha$ We can not assume that either $f$ nor $g$ are convex, on the contrary - we can assume they are ...
104 views

### How to solve a DC (Difference of Convex) program?

I have an objective function which is the difference of two convex functions in Tensorflow and I want to minimize it. Formally, I have the following problem: \$\text{min}_{x \in \mathcal{X}} \;\;f(x)-...