Skip to main content

# Questions tagged [non-convex-optimization]

A non-convex optimization problem is one where either the objective function is non-convex in a minimization problem (or non-concave in a maximization problem) or where the feasible region is not convex.

674 questions
Filter by
Sorted by
Tagged with
0 votes
0 answers
4 views

### Non-convex programming

I want to solve a non-convex optimization problem of the form : \begin{array}{cl} \displaystyle \min_{x} & f(x)\\ \textrm{s.t.} & c(x) = 0,\\ \end{array} where $f$ is a concave smooth function ...
• 11
1 vote
0 answers
64 views

• 691
1 vote
0 answers
58 views

• 53
0 votes
0 answers
28 views

### Is it possible to convexify the inequality constraint $z \leq x^3 \cdot y$?

Is there a way to convexify the inequality constraint $z \leq x^3 \cdot y$ in a nonlinear optimization problem with $x, y, z$ being nonnegative variables?
• 53
0 votes
1 answer
43 views

• 51
1 vote
1 answer
66 views

• 53
1 vote
2 answers
85 views

### A simple constrained optimization problem

Let $v\in \mathbb{R}^n$. Define $E(v) = \sum_{i=1}^n (v_i^2-1)^2$ be the energy to be minimized. Define the constraint $\sum_{i=1}^n v_i = cn$. This means the average value of all $v_i$'s is $c$. ...
• 2,039
1 vote
1 answer
49 views

0 votes
0 answers
53 views

### Dynamics of Loss in Homogeneous, Non-Smooth Models Using Clarke Subdifferential

tl;dr: Seeking insights on the application of Clarke subdifferential for analyzing the optimization differential inclusion with smooth objective and homogeneous model. I'm interested in its validity, ...
• 8,361
1 vote
2 answers
114 views

### Proof or counterexample for the convergence of projected gradient descent with summable stepsizes

Suppose we want to solve the following optimization problem: $$\min_{x\in\mathcal{X}\subset\mathbb{R}^n} f(x)$$ where $\mathcal{X}$ is closed and convex and $f$ can be nonconvex but still smooth. ...
• 33
0 votes
1 answer
135 views

• 562