Skip to main content
Share Your Experience: Take the 2024 Developer Survey

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.

Filter by
Sorted by
Tagged with
1 vote
2 answers
428 views

optimizing piecewise linear objective functions (perhaps non convex) with equality constraints

When I do my project, I need to optimize piecewise linear objective functions (perhaps non convex) with equality constraints. The piecewise linear objective function may be not convex like this in the ...
Yiyuan Chen's user avatar
0 votes
0 answers
53 views

Linear Programming with bounds on magnitude

I have a set of halfplanes $H$, and a target vector $T$. My goal is to find the vector $v$ closest (2-norm) to vector $T$, such that $v$ is in the intersection of all of the halfplanes. This can be ...
Nicholas Pipitone's user avatar
0 votes
0 answers
49 views

Deriving the Cauchy point of the horizontal subproblem for large-scale trust-region SQP

I am having difficulty deriving the Cauchy point of the horizontal subproblem $$ \overline{g}_k^T Z_k u + \frac{1}{2} u^T Z_k^T W_k Z_k u \;\;\;\;\mbox{subject to}\;\; \mid \mid Z_k u \mid\mid_2 $$ ...
Olumide's user avatar
  • 285
1 vote
0 answers
66 views

min(f(x)) is convex or concave based on type of f(x)

i have f(x) that is concave function. My question is g=min(f(x)) is concave or convex? And max(g) is concave or convex? there is a theorem for this?
Maria's user avatar
  • 11
1 vote
0 answers
64 views

How to show that the solution of the following quadratic programming is non-negative

I have the following quadratic problem: $max$ $a^Tx+0.5x^TAx$ $s.t: 1^Tx=1$ in which $a=[a_1, a_2,...,a_n]$ is a non-negative vector, and $1^T=[1,1, ..., 1]$. The hessian matrix $A$ has the ...
user45682's user avatar
3 votes
0 answers
203 views

Python code of explicit method of a nonlinear a BVP

I am trying to have a Python code for the following nonlinear BVP: $$\frac{\partial N}{\partial t}=\frac{\partial^2 N}{\partial x^2}+N(1-N)-\sigma N$$ $$N(0,x)=\sin(2\pi x)$$ $$N(t,0)=0 \hspace{3mm}N(...
Peachy April's user avatar
2 votes
0 answers
98 views

Can we get the exact solution of large-scale quadratic programming problems (quadratic objective, linear inequality constraints) using KKT condition?

Crossposted at MathOverflow Consider a quadratic programming problem with the following format: $$ \text{min} Q(x) = c^Tx+\frac{1}{2}x^TDx \\ $$ $$ \text{s.t.} Ax\leq b, \\ x\geq 0 $$ where $D$ is a $...
ximeng fan's user avatar
3 votes
1 answer
94 views

A question related with $p$-Laplacian and conjugate gradient method

I have the following energy functional of $p$-Laplacian equation: $$ E(u) = \frac{1}{p} \int_{\Omega} |\nabla u|^p dx $$ for $2.8 \leq p \leq 5$. My goal is to minimize the energy functional by using ...
User124356's user avatar
0 votes
0 answers
81 views

Automatic differentiation necessary for large optimal control problems?

I am investigating ways to solve an optimal control problem in an embedded way, preferably in Java. The system is modeled with triple integrator dynamics $u=\dddot{x}$ and solved with multiple ...
SAVG8778's user avatar
-1 votes
1 answer
79 views

RobOptim for real-time computation

Do you think that the RobOptim optimization library (which I read about in C++ library for nonlinear constrained minimization) could be used for real-time optimization for the velocity control of a ...
Eugenio Monari's user avatar
1 vote
0 answers
44 views

Solving the non-linear Hamiltonian using Scipy's root finding method

I am a complete novice to computational physics and am finding difficulty in implementing a code to iteratively solve for a $2\times2$ nonlinear Hamiltonian using Scipy's root solver. I can't seem to ...
hello_world30's user avatar
2 votes
1 answer
126 views

Linearize problem with absolute value

Is there any method to linearize the following optimization problem? \begin{align} min_{x,y} &~~ c~[x; y] \\ st &~~ \sum x\leq \alpha_1 \\ &~~ \sum |y|\leq \alpha_2 \\ &~~ \sum y= 0 \\ ...
Reda's user avatar
  • 121
2 votes
0 answers
104 views

Cyipopt fails to converge for NLP problem which fmincon() can solve

I'm currently trying to implement a python script for solving a constrained nonlinear optimization problem with ~800 variables and 2 constraints, one linear and one nonlinear. There already exists a ...
Bobbybobbobbo's user avatar
0 votes
0 answers
174 views

How to implement large rotations in total lagrangian formulation (nonlinear FEM)?

I have developed an Octave script to solve the nonlinear Euler-Bernoulli beam equations with linearized von Karman-strains, i.e. higher-order terms are dropped. The simulation results agree with ...
Tepa's user avatar
  • 31
1 vote
0 answers
202 views

Fitting data with a Voigt function

I have some data, (xrd data), that I would like peak fit with a pseudo-Voigt function, a combination of a Gaussian and a Lorentzian function. These are the functions $G(x) = I \exp\left( -\frac{4\ln(2)...
Peter's user avatar
  • 33
1 vote
0 answers
58 views

Hessian-free preconditioner for non linear least squares

I am solving a nonlinear least squares problem using Gauss Newton method. Due to the large dimension of the problem, I use the Hessian-free approach. As a linear solver I use either MINRES or CG. To ...
Aleksandr Borisov's user avatar
2 votes
0 answers
50 views

Looking for a library for solving convex-convex quadratic fractional programming problems

Is there a library of some programming language (MatLab, C, Python, R, etc.) that includes a function for efficient calculation of convex-convex quadratic fractional programming problems of the form $$...
Evan Aad's user avatar
  • 121
3 votes
1 answer
144 views

Applying displacement control loading using lagrange multipliers in the material non-linear finite element method

Hi I am trying to implement a simple plasticity based finite element code. I am not clear how to set up displacement control applied through Lagrange multipliers. In case of a linear problem, I did ...
Bruce Lee Jun Fan's user avatar
2 votes
0 answers
141 views

Parametric nonlinear programming

I believe, I have a parametric nonlinear optimization problem. The non-convex constraints depend on some parameters, and I seek a solution that satisfies these constraints for all parameters in a ...
vaiana's user avatar
  • 21
0 votes
0 answers
187 views

Phase portrait of non-linear system of ode (Triple Galaxy System)

Context: Hello, I am an undergrad student of physics self-studying Python Programming. I am trying to find the value of H_lam for which limit cycles corresponding ...
Nirmal Padwal's user avatar
2 votes
0 answers
62 views

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 ...
RockedSalad121's user avatar
0 votes
1 answer
353 views

Avalability of SNOPT optimization solver

I'd like to know if SNOPT solver is available free of cost for academic research in any of the optimization software packages. I came across a few softwares that have SNOPT, but those require a ...
Natasha's user avatar
  • 421
4 votes
1 answer
315 views

What's the right choice of variable settings for setting up my optimal control problem?

This is a followup to my previous question here I have the following dynamical system, $\frac{d \phi}{dt} = -M^TDM\phi \tag{1}\label{1}$ $\frac{d \hat\phi}{dt} = -M^T\tilde{D}M\hat \phi \tag{2} \...
Natasha's user avatar
  • 421
3 votes
1 answer
1k views

Setting up optimization problem in GEKKO

I have the following dynamical system, $\frac{d \phi}{dt} = -M^TDM\phi \tag{1}\label{1}$ $\frac{d \hat\phi}{dt} = -M^T\tilde{D}M\hat \phi \tag{2} \label{2}$ $\eqref{1}$ represents the exact ...
Natasha's user avatar
  • 421
3 votes
0 answers
244 views

Automatically generate constraints for trajectory optimization

This is a follow up to my previous post here I'm interested in performing trajectory optimization from the problem mentioned in abov link. I want to supply the following as dynamical constraints to ...
Natasha's user avatar
  • 421
1 vote
2 answers
186 views

Solving a parameter estimation problem using trajectory optimization

This is a follow-up to my previous question here I've the following system of equations for studying information flow in the below graph, $$ \frac{d \phi}{dt} = -M^TDM\phi + \text{noise ...
Natasha's user avatar
  • 421
3 votes
0 answers
101 views

Large-scale optimization of nonlinear equations

I'm looking to find a computationally efficient solution to a large system of nonlinear equations. I'm trying to maximize the following function: $$ f(\vec{x}) = \sum_i^N C_i (x_i-A_i)x_i^{\epsilon_{...
alexvas's user avatar
  • 203
5 votes
2 answers
917 views

MINLP with GEKKO - Modeling discrete variables

I'm trying to define a MINLP optimization problem with GEKKO in Python, and I want to use some variables with fixed values. For my first variable, x1, I need to define the following values (as would ...
srgam's user avatar
  • 245
1 vote
1 answer
717 views

Preconditionning for solving a non-linear system of equations with least squares

I am trying to solve a large system of non-linear equations (about a few hundred equations and variable but with less variable than equations). Given that the system is really sparse and large I am ...
yjn's user avatar
  • 27
3 votes
0 answers
60 views

How to set up and solve acceleration-limited trajectory optimization problems?

I've been trying to learn how to solve simple acceleration-limited trajectory planning problems. I'm working in C++ and I've been using the Eigen library to do linear systems solving. I'm doing the ...
James McNeill's user avatar
4 votes
1 answer
99 views

Geometric Programming - symbolic version

I am interested in finding minimizers of functionals of the type $\sum x^ay^bz^c$ where the exponents are 1, 0 or -1. I have codes to find such minimizers when they exist up to machine precision, ...
Beni Bogosel's user avatar
  • 1,057
1 vote
0 answers
54 views

Finite dimensional optimization problem over dynamical system

I am interested in solving numerically the following mathematical problem Consider an ode of the form $$ \dot q(t) = f(q(t),t_1,\ldots, t_N),\qquad t\in [0,T], $$ where $q\in \mathbb{R}^n$ is the ...
Smilia's user avatar
  • 468
3 votes
1 answer
135 views

Nonlinear conjugate gradient with orthogonality constraint

I have to solve a set of nonlinear optimization problems in the subspace defined as the orthogonal space to a given vector. More precisely, $$ \arg\min f(\vec x) \qquad \text{with} \qquad \vec x \...
skdys's user avatar
  • 171
1 vote
0 answers
110 views

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 ...
computational_scientist's user avatar
1 vote
1 answer
77 views

Research articles on MultiObjective Non-Linear Programming (MONLP)

I'm looking for papers dealing with multi-objective non-linear programming which could help me implement an algorithm to solve my problem. My problem is : Maximize $f(x) = c \cdot x$, while ...
Pierre Gourseaud's user avatar
-2 votes
1 answer
150 views

Gradient line-search Matlab code gets stuck [closed]

...
HybridAlien's user avatar
0 votes
1 answer
46 views

Slightly change two vectors to satisfy a constraint

$\vec{a}\cdot\vec{b} \approx c$ $\vec{\alpha} \cdot \vec{\beta} = c$ $\vec{\alpha}$ is close to $\vec{a}$ and $\vec{\beta}$ is close to $\vec{b}$ Given $\vec{a}$, $\vec{b}$ and c, how to find $\vec{\...
R zu's user avatar
  • 163
1 vote
1 answer
1k views

Why does Newton's method with Linear Equality Constraints use KKT condition?

Goal: Optimize convex function $f(\vec{x})$ subjected to constraint $A\vec{x} = \vec{b}$ starting at a point $\vec{x}_0$ that satisfies the constraint. The problem only has equality constraint. Why ...
R zu's user avatar
  • 163
1 vote
1 answer
452 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 ...
rhaskett's user avatar
  • 113
2 votes
0 answers
293 views

Convergence of a very large non-linear least squares optimization

(note: I also posted this question on stackoverflow before finding this community here, which seems a better place for it) I'm trying to solve the following problem: I have a lot (~80000) surface ...
mrburnst's user avatar
4 votes
1 answer
520 views

How to solve the following Frobenius norm-minimization problem?

Background We know how to solve the following minimization problem $$ \min_{X} \lVert AX - B \rVert_F^2 $$ But what about the extended version? $$ \min_{X} \lVert A \begin{bmatrix} X & X^2 \...
ArtificiallyIntelligent's user avatar
2 votes
1 answer
139 views

Nonlinear least square optimization

Problem description Given data at many time instance $t$, $$\min _{\alpha, \Lambda, \beta} \lVert y(t) - \alpha e^{\Lambda t} \beta \rVert_F$$ with $$ \lVert \alpha \rVert_2^F = 1 $$ where $y(t) \...
ArtificiallyIntelligent's user avatar
2 votes
1 answer
225 views

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: ...
user1372338's user avatar
0 votes
1 answer
69 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 ...
jjjjjj's user avatar
  • 325
3 votes
1 answer
334 views

Obtaining a feasible solution for underdetermined system of linear equations satisfying inequality constraints

I would like to obtain a feasible solution for an under-determined system of linear equations, $$Ax=b$$ where, $A \in \mathbb{R}^{7\times9}, \, x \in \mathbb{R}^{9\times1}\text{and } b\in\mathbb{R}^...
Dr Krishnakumar Gopalakrishnan's user avatar
2 votes
0 answers
59 views

Nonlinear Sylvester-Like Equation

Maybe you can point me to some results already developed for this. I have to solve for $X$ the following "Sylvester-like" equation: $$ AX - XB = F(X)$$ where $A\in\mathbb{R}^{a\times n}$, $B\in\...
Nico F.'s user avatar
  • 121
1 vote
0 answers
103 views

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 ...
Michael's user avatar
  • 417
0 votes
1 answer
89 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 ...
rasalghul's user avatar
1 vote
1 answer
156 views

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 ...
Electrode's user avatar
4 votes
1 answer
525 views

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 ...
wyer33's user avatar
  • 767