# Questions tagged [nonlinear-programming]

Questions about the theory and numerical algorithms for optimizing (minimizing or maximizing) nonlinear functions, possibly subject to equality and/or inequality constraints.

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### Could not get expected result?

I am trying to solve the example 3.3 in this book. ...
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### Need Help for Formulating in YALMIP

I want to implement the given optimization algorithm for the ieee-14 bus system into YALMIP. It is a non-convex type of problem. it will be appreciated if anyone can help me in formulating this into ...
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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 ...
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### How to multiply 2 decision variables and a matrix using python

So, basically our agenda is to assign tour guides to tour groups based on this equation and that will be done by these 2 decision variables z(u,g) and y(g,p) where z(u,g) will be 1 if tour guide 'u' ...
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### Tikhonov regularization in the non-negative least square - NNLS (python:scipy)

I am working on a project that I need to add a regularization into the NNLS algorithm. Is there a way to add the Tikhonov regularization into the NNLS implementation of scipy ?  talks about it, ...
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### Correct way to model an embedded reinforcement (non linear FEM)?

I need to add to an existing FEM solver some embedded reinforcement element. This would give me the possibility to model/solve concrete structure (reinforced with steel rebar) taking into account the ...
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### Connection between piecewise linear basis functions and RELU activation function

ReLU activation is defined as follows $$\sigma(x)=\max(0, x).$$ Let's assume that I have deep network of 1 hidden layer, than output from my layer has form $$f(x)= \sigma(Wx +b),$$ where matrix W ...
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### Is there a high quality nonlinear programming solver for Python?

I have several challenging non-convex global optimization problems to solve. Currently I use MATLAB's Optimization Toolbox (specifically, fmincon() with algorithm=<...
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### Constraints 'exactly/at most one non-zero element' without binary variables

In a much larger MINLP problem, I have set of variables $\{a_{ij}\}_{m,n}$, such that $0 \leq a_{ij} \leq 1$ for all $i$, $j$, which I could think of as a matrix, for which I have two requirements: ...
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### GAMS solvers: which one to use

The other day I had a discussion with a friend about the GAMS solvers and we were wondering what are the mathematical differences between the solvers. Which one to use for which kind of problem? How ...
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### Optimization with matrix determinant as constraint

I'm solving a constrained optimization for matrix $\mathbf{A}$ with dimension 6x6, where one of the constraints is $\mathrm{det}(\mathbf{A})>0$. I use the NLopt package to solve my problem and ...
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### 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 ...
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### How can i solve this non-convex multi-variable optimization problem?

I want to solve the following optimization problem: $$\min_{A,B,X} \|Y-AX\|_F^2 + \lambda_1 \|Z-BX\|_F^2+ \lambda_2 \|B\|_F^2$$ $$s.t ~~x_{ij}~ \geq 0$$ in which, $Y$ and $Z$ are data matrices and ...
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### Direct multiple shooting (numerical optimal control)

Please, I am currently implementing direct multiple shooting methods* and I need one simple but fundamental concept answered: When I want to provide not only objective function value (the result of ...
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### Nonlinear global optimization algorithm that can use dynamic programming

I've asked this question on stackoverflow 2 weeks ago, but, judging by zero response, that probably was the wrong forum. Therefore copying it here: Let F0,...,Fn ...
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### Why do active set methods or the simplex method pivot only one variable at a time?

Why do active set methods or the simplex method pivot only one variable at a time? Ostensibly, we could add multiple columns to the basis during pivoting, but the standard presentation of the methods ...
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### 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 ...
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Suppose $A\in\mathbb{R}_+^{n\times n}$ is symmetric. I would like to factorize $A\approx UU^\top$ by solving $$\begin{array}{rl} \min_U & \sum_{ij} \left(A_{ij}\ln\frac{A_{ij}}{[UU^\top]_{ij}}+[... 1answer 92 views ### L_2 projection with integer constraints and prescribed sum Suppose I am given a vector v^0\in\mathbb{R}^n and integers k,\ell\in\mathbb{Z}. Assuming k is close to zero (e.g. 0\leq k\leq5), is there an algorithm for solving the following integer ... 0answers 56 views ### Object-oriented non-linear solving in python I'd like to build a system in Python, consisting of (broadly speaking) objects which are internally described with (not necessarily just linear) equations, that I can connect with each other - similar ... 0answers 70 views ### Minimizing the products of variables My problem Maximize$$\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}...
I have 3 functions which consist of 6 variables $p_1,p_2,p_3,p_4,p_5,p_6$. The value of each function is equal to $x$ (say): \begin{align} f_1 &= \operatorname{sign}(2-p_1) \sqrt{|2-p_1|} + \...
For the optimization problem $\underset{\mathbf{x}\in \mathbb{R}^n}{\operatorname{argmin}} f(\mathbf{x})$, we can use the following standard nonlinear conjugate gradient method to find the solution: \$...