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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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
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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
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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
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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
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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
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Estimating/Tuning a Coefficient from a Quadratic Programming Objective Function so Optimal Solution Reflects Data

I am working on a problem that is a modified version of a two-knapsack knapsack problem. I am able to find the optimal choices by using Gurobi. However, I would like to estimate a coefficient that is ...
Jack Keefer's user avatar
2 votes
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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
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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
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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
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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
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41 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
99 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
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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
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163 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
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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
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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
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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
137 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
140 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
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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
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1 answer
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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
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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
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3 votes
1 answer
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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
239 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
174 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
96 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
  • 193
5 votes
2 answers
847 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
682 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
55 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
96 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 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
  • 269
3 votes
1 answer
133 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
  • 161
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
143 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
441 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
292 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
505 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 \...
ArtificiallyIntelligence's user avatar
2 votes
1 answer
137 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) \...
ArtificiallyIntelligence's user avatar
2 votes
1 answer
202 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
292 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
101 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
86 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
155 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
502 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
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