# Tag Info

Accepted

### Global convergence in trust region algorithm

Standard terminology in nonlinear (i.e., derivative-based) optimization is that "global convergence" means "convergence to a stationary point no matter where you start from" (where the limit may in ...
• 12.3k

### Is there an optimization scheme/algorithm that converges, for this non-convex scenario but with some special properties

Despite your claim that these functions have "special properties", the properties you've supplied still leave f and g extremely ...
• 4,011
Accepted

### A robust algorithm to sort a non-convex polygon vertices

As @HighPerformanceMark mentioned in the comments if the set of vertices $V=\{v_0,\ldots,v_{N-1}\}$ is the only information you have about your non-convex polygon, you did not define it uniquely. One ...
• 8,702
Accepted

### Symmetric nonnegative matrix factorization

I'm going through some of my old StackExchange posts and came across this one. As it turns out, the answer led to a section in a published paper! As detailed in that paper (and in its notation), if ...
• 1,413
Accepted

### Piecewise-Linear Quadratic Optimization for an "Almost Convex" Problem

You could implement the piecewise linear functions using SOS2 variables (SOS2=Special Ordered Sets of Type 2). This approach does not care about convexity (that is, convexity related to the piecewise ...
Accepted

### Why can't we discretize continuous domains in distributed non-convex constraint optimization problems?

You are missing that, in general, integer optimization problems are much more expensive to solve than real-valued optimization problems. That's because for real-values optimization problems, you have ...
• 56.1k
Accepted

### Optimization of non-smooth, non-convex, locally Lipschitz functions of type exp(-abs(x))

I think I found the right article myself: Lewis, A.S. & Overton, M.L. Math. Program. (2013) 141: 135. doi:10.1007/s10107-012-0514-2
• 193

### How to formulate a convex expression to minimize the difference between Frobenius norm of a positive semidefinite matrix and a positive value

One solution to the problem is to choose $P$ as the diagonal matrix with diagonal entries equal to $J/\sqrt{n}$. Its Frobenius norm is $J$ and it is symmetric and positive definite.
• 56.1k

### How to solve a 4th order nonnegative LASSO problem?

I guess a problem with this approach is that it also "sparsifies" the gradient. If you look at the objective function: \begin{align} \Phi(x) = \lvert|(Ax)\odot(Ax)-b |\rvert^2+\lambda\lvert|...
• 725
1 vote

### reduced system: primal-dual interior point method for nonconvex constrained problem

Once you have $p_x,p_y$, you can use the second and fourth of the block system you show in your question to compute the updates $p_s,p_z$. They satisfy the equations \begin{align} \begin{bmatrix} \...
• 56.1k
1 vote

### Why should non-convexity be a problem in optimization?

This is an indirect answer. Other answers already explain in detail why it is that non-convex optimization is challenging, but to recap: No solution method we have, other than brute force, is ...
• 4,011
1 vote

### Why should non-convexity be a problem in optimization?

In addition to the answers already given an additional issue is that without convexity the Hessian is not guaranteed to be positive definite. This complicates any method using a quadratic model (such ...
• 183
1 vote

### Minimal surface finite differences problem - Matlab assemble

Here is a fast implementation using sparse matrices and sparse Jacobian estimation: ...

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