# Questions tagged [nonconvex]

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### Minimal surface finite differences problem - Matlab assemble

I face to the following problem: $$(1+u_x^2)u_{yy} - 2u_xu_yu_{xy} + (1+u_y^2)u_{xx}=0.$$ Problem needs to be discretized and assembled. Does anybody know how to proceed in Matlab?
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### Black box optimization

I have a simulation which gives a scalar result depending on the choice of some continuous design variables. I am trying to minimize the output of the simulation. As a first step, I want to study the ...
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### How to solve a 4th order nonnegative LASSO problem?

I need to solve the following 4th order nonnegative LASSO problem: $$\min_{x \geq 0} \quad || |Ax|^2 - b ||^2 + \lambda ||x||_1$$ where $|\cdot|^2$ denotes element-wise squared. $A$ is small size (e....
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### Convergence of Truncated Newton for non-convex Hessian

I was wondering if anyone could enlighten me about the convergence properties of the truncated newton method in case of a non-positive definite hessian $\nabla^2 f = H$. From the Book 'Numerical ...
109 views

### Proving convexity of Frobenius norm and correlation function formulations of an optimization problem

I have been working on formulating my requirements in the form of an optimization problem in a multi-output regression setting. Firstly, I would like to make the variables I used in the problem and ...
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### Ramp least squares estimation

With some given $s$ value, let \begin{aligned} h(\beta)&=\min(\sum_{i=1}^n(Y_i - X_i\beta)^2, s)\\ &=\sum_{i=1}^n(Y_i - X_i\beta)^2-\max(0, \sum_{i=1}^n(Y_i - X_i\beta)...
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### Global optimization with known distributions of some variables

I'm solving simple single-objective multidimensional global optimization problem using various stochastic algorithms like Monte-Carlo, GA and other evolutionary approaches. The task is formulated as ...
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### preconditioning LBFGS?

I want to minimize an energy of the form $$V_1(\mathbf{x}) + V_2(\mathbf{x})$$ where $V_1$ is much stiffer than $V_2$. When I try to use LBFGS, convergence is extremely slow, as the solution ...
258 views

### Numerical solution of non-linear advection equation other than inviscid burgers

I am solving a non-linear advection equation of the form $u_t + f(u)_x = 0$ where $f(u)$ is a complicated function of $u$. I am solving this equation using a first order fully implicit scheme (...
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### Global convergence in trust region algorithm

I was reading about TR methods and there are some terms, which are confusing for me. It says, method is globaly convergent. What does it really mean? Converges to global minima, or converges for ...
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### Minimization of the sum of convex function and non-linear non convex function

I'm trying to minimize the unconstrained scalar sum of a quadratic convex function (to which a convex optimizer is readily applied) and a non-linear and non-convex function which is differentiable. ...
2k views

In these notes (section 2.3), it is stated that: A point $x^*$ is a minimizer of a function $f$ (not necessarily convex) if and only if $f$ is subdifferentiable at $x^*$ and $0 \in\partial f(x^*).$ ...
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### linear independence constraint qualification: what to do when they don't hold?

I want to solve a general nonlinear constrained optimization problem $$\min_q\ f(q)\quad \textrm{s.t.}\quad g_i(q) = 0,\ h_j(q) \geq 0.$$ The problem is that while the equality constraints $g_i(q)$ ...
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### non convex, non linear optimization involving matrix differential equation solution

I'm trying to develop an inferential procedure for a multivariate dependent Markov process. Basically, the procedure could be considered as a non linear regression, with a known dependence structure ...
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### Nonconvex Optimization

Consider the following optimization problem: $\text{max}_{p} \quad ||p||^2 \\ s.t: x\geq 0\\ p\in D$ where $D$ is a convex set. Is this problem $\mathcal{NP}$-hard?
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### Affect of approximating a non-differentiable function on optimisation of minimisation

I am looking at a problem of constrained minimization, where the function to be minimized contains the Heaviside function, and as such is not twice continuously differentiable. My question is what ...
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### Non convex optimization

I have the following Max Min optimization problem that appears to be non convex. link where t p c are my variables and all others are constants. I took the eigen values of the hermetian part of the ...
I'm looking at a global minimisation problem on the $n$-sphere ($n$ of the order 10--50) but with a complete swine of an objective --- it is (effectively) a black box; it is piecewise smooth but with ...