Stack Exchange Network

Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [nonconvex]

The tag has no usage guidance.

1
vote
0answers
31 views

Efficient numerical optimization of an “almost separable” function

I have come across an optimization problem with the following objective function: $$f(x_0,y_0,z_0,x_1,y_1,z_1,...,x_N,y_N,z_N) = \sum_{i=0}^N f_i(x_i,y_i,z_i, \alpha(x_{i+1}-x_i) + \beta(y_{i+1}-y_i))...
1
vote
1answer
78 views

Piecewise-Linear Quadratic Optimization for an “Almost Convex” Problem

I have a 7-14 dimensional piecewise linear cost function I'd like to minimize with two quadratic terms of the form: $$ f(X) = X^tCX + d \sum_i |x_i-x^*_i|^2 + \sum_i P_i(x_i-x^0_i) $$ $$ \sum_i x_i ...
0
votes
0answers
55 views

Artificial Neural Network for nonconvex optimization

I want to use artificial neural network(ANN) for solving non-convex optimisation problems. How do I map the constraints and the objective functions in the ANN architecture?
0
votes
1answer
54 views

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

When solving a reduced KKT system of a nonlinear (and nonconvex) constrained program after eliminating slack and dual variables, how do we actually take the next step in a primal-dual method? For ...
0
votes
1answer
55 views

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

Consider a non-convex distributed optimization problem. We have $X$ = a set of $n$ decision variables: $x_i$ where $i=1..n$ and $x_i \in R$, the set of Reals. We have $F$ = a set of $m$ constraint ...
1
vote
0answers
61 views

Minimizing the products of variables

My problem Maximize $$\min_{i} \{\ c_i \cdot \prod_{j \in A(i)} {x_{j}} \prod_{j \in B(i)} {y_{j}} \} $$ Subject to \begin{align} &\sum_{j \in C(k)} x_{j} = 1,\ \forall k \\ &l \leq x_{j}...
1
vote
0answers
159 views

Constrained optimization: Stationary point vs. Nash point

1s question: definition of stationary point for constrained optimization As far as I know, a stationary point of a constrained optimization problem is a stationary point of the Lagrangian (that has ...
5
votes
1answer
134 views

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

What would be the numerical method of choice to find minima in a non-smooth, non-convex, locally Lipschitz function $f: \mathbb{R}^n\rightarrow \mathbb{R}$. The function $f$ is mostly smooth but ...
2
votes
0answers
60 views

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 ...
2
votes
2answers
155 views

Approach to handle a quadratic constraint xy <= z

I have non-linear constraints like $ x_1x_2\leq x_3 $ where $ x_1,x_2,x_3\geq 0 $. The objective is linear, and all other constraints are linear, too. I know that I can transform the product as $ ...
1
vote
0answers
92 views

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 ...
5
votes
1answer
333 views

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 ...
1
vote
0answers
199 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 (...
18
votes
3answers
6k views

Why should non-convexity be a problem in optimization?

I was very surprised when I started to read something about non-convex optimization in general and I saw statements like this: Many practical problems of importance are non-convex, and most non-...
1
vote
0answers
117 views

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. ...
4
votes
2answers
1k views

Subgradients of non-convex functions

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 $0 \in\partial f(x^*).$ ...
3
votes
1answer
209 views

Symmetric nonnegative matrix factorization

Suppose $A\in\mathbb{R}_+^{n\times n}$ is symmetric. I would like to factorize $A\approx UU^\top$ by solving $$ \begin{array}{rl} \min_U & \sum_{ij} \left(A_{ij}\ln\frac{A_{ij}}{[UU^\top]_{ij}}+[...
2
votes
0answers
88 views

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 ...
1
vote
0answers
175 views

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?
2
votes
0answers
341 views

Finite difference scheme for solving nonlinear least-squares problem

I am dealing with following problem: $$ \min_{u,\gamma}\Bigg\{ \frac{1}{1000} \iint_{S_2} {\gamma (x,y)^2 dxdy} + \iint_{S_2} {[u(x,y) - u_0 (x,y)]^2 dxdy} + \iint_{S_2} {[\Delta u(x,y) - \gamma (...
4
votes
2answers
167 views

non-convex quadratic with only one quadratic constraint?

I have a non-convex optimization problem in the form: \begin{align} \min_{b,\xi,\eta} \sum_{i=1}^{n} b_i \xi_i + \gamma \Vert \eta \Vert \cr \text{s.t.} b\geq 0, b^\mathsf{T} 1 = 1,b_i \leq \frac{1}{n-...
4
votes
2answers
546 views

Finding a global minimum of non-convex quasi-smooth function that is costly to evaluate

I have a bounded non-convex function in 10-dimensional space. The function is quasi-smooth, you can imagine a histogram, here is an illustration, it just shows the idea and not related to my ...
5
votes
2answers
205 views

Is there guaranteed global solver for such an eigenvalue problem?

The original nonlinear optimization problem I have is as follows: For constant symmetric matrices $A=A^T, B_i=B_i^T(\forall i\in\mathbb{N}) \in \mathbb{R}^{n\times n}, \text{rank}(A)=n,$ $$\arg\min\...
0
votes
2answers
115 views

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?
3
votes
2answers
479 views

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 ...
0
votes
1answer
402 views

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 ...
6
votes
2answers
2k views

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 $g_i(q)$ ...
2
votes
3answers
861 views

Global optimisation with discontinuous objective

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 ...
1
vote
0answers
19 views

Reduction for NP-hardness [duplicate]

Consider the following optimization problem: \begin{align} \text{Min}_{i\neq j\neq s\neq t} |x_i x_j-x_sx_t|\\ s.t: Ax=b\\ x\geq 0; \end{align} This problem can be seen as an instance of non convex ...
3
votes
2answers
685 views

NP-Completeness

Consider an instance of non-convexoptimization problem: It seems that this problem is NP-complete. How can I find a suitable reduction for this?
6
votes
1answer
233 views

Algorithm for dealing with medium-size non-convex QCQP

I have the following problem in $x \in \mathbb C^{205}$ $$\displaystyle\min_{x}x^HAx$$ subject to the following constraints $$x^HBx = 1$$ $$x^HC_ix = 0$$ for $i \in \{0,1,\dots,203\}$, where $A$ ...