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.
146
questions
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0
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49
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 ...
0
votes
0
answers
47
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
$$
\overline{g}_k^T Z_k u + \frac{1}{2} u^T Z_k^T W_k Z_k u \;\;\;\;\mbox{subject to}\;\; \mid \mid Z_k u \mid\mid_2
$$
...
- 255
1
vote
0
answers
63
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?
- 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 ...
- 11
3
votes
0
answers
155
views
Python code of explicit method of a nonlinear a BVP
I am trying to have a Python code for the following nonlinear BVP:
$$\frac{\partial N}{\partial t}=\frac{\partial^2 N}{\partial x^2}+N(1-N)-\sigma N$$ $$N(0,x)=\sin(2\pi x)$$
$$N(t,0)=0 \hspace{3mm}N(...
- 31
0
votes
0
answers
11
views
Estimating/Tuning a Coefficient from a Quadratic Programming Objective Function so Optimal Solution Reflects Data
I am working on a problem that is a modified version of a two-knapsack knapsack problem. I am able to find the optimal choices by using Gurobi. However, I would like to estimate a coefficient that is ...
2
votes
0
answers
97
views
Can we get the exact solution of large-scale quadratic programming problems (quadratic objective, linear inequality constraints) using KKT condition?
Crossposted at MathOverflow
Consider a quadratic programming problem with the following format:
$$
\text{min} Q(x) = c^Tx+\frac{1}{2}x^TDx \\
$$
$$
\text{s.t.} Ax\leq b, \\
x\geq 0
$$
where $D$ is a $...
- 21
3
votes
1
answer
89
views
A question related with $p$-Laplacian and conjugate gradient method
I have the following energy functional of $p$-Laplacian equation:
$$
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 ...
- 143
0
votes
0
answers
76
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 ...
- 1
-1
votes
1
answer
78
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 ...
1
vote
0
answers
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 ...
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 \\
...
- 121
2
votes
0
answers
98
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 ...
0
votes
0
answers
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 ...
- 31
1
vote
0
answers
182
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)...
- 33
1
vote
0
answers
55
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 ...
2
votes
0
answers
48
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
$$...
- 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 ...
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 ...
- 21
0
votes
0
answers
182
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 ...
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 ...
0
votes
1
answer
292
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 ...
- 421
4
votes
1
answer
297
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} \...
- 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 ...
- 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 ...
- 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,
$$ \frac{d \phi}{dt} = -M^TDM\phi + \text{noise ...
- 421
3
votes
0
answers
96
views
Large-scale optimization of nonlinear equations
I'm looking to find a computationally efficient solution to a large system of nonlinear equations. I'm trying to maximize the following function:
$$ f(\vec{x}) = \sum_i^N C_i (x_i-A_i)x_i^{\epsilon_{...
- 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 ...
- 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 ...
- 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 ...
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, ...
- 985
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 ...
- 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,
$$
\arg\min f(\vec x) \qquad \text{with} \qquad \vec x \...
- 161
1
vote
0
answers
110
views
Connection between piecewise linear basis functions and RELU activation function
ReLU activation is defined as follows
$$\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), $$
where matrix W ...
1
vote
1
answer
77
views
Research articles on MultiObjective Non-Linear Programming (MONLP)
I'm looking for papers dealing with multi-objective non-linear programming which could help me implement an algorithm to solve my problem.
My problem is :
Maximize $f(x) = c \cdot x$, while ...
- 121
-2
votes
1
answer
143
views
0
votes
1
answer
46
views
Slightly change two vectors to satisfy a constraint
$\vec{a}\cdot\vec{b} \approx c$
$\vec{\alpha} \cdot \vec{\beta} = c$
$\vec{\alpha}$ is close to $\vec{a}$ and $\vec{\beta}$ is close to $\vec{b}$
Given $\vec{a}$, $\vec{b}$ and c, how to find $\vec{\...
- 163
1
vote
1
answer
1k
views
Why does Newton's method with Linear Equality Constraints use KKT condition?
Goal: Optimize convex function $f(\vec{x})$ subjected to constraint $A\vec{x} = \vec{b}$ starting at a point $\vec{x}_0$ that satisfies the constraint.
The problem only has equality constraint. Why ...
- 163
1
vote
1
answer
441
views
Piecewise-Linear Quadratic Optimization for an "Almost Convex" Problem
I have a 7-14 dimensional piecewise linear cost function I'd like to minimize with two quadratic terms of the form:
$$
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 ...
- 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 ...
- 31
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?
$$
\min_{X} \lVert A
\begin{bmatrix}
X & X^2
\...
2
votes
1
answer
137
views
Nonlinear least square optimization
Problem description
Given data at many time instance $t$,
$$\min _{\alpha, \Lambda, \beta} \lVert y(t) - \alpha e^{\Lambda t} \beta \rVert_F$$
with $$ \lVert \alpha \rVert_2^F = 1 $$
where $y(t) \...
2
votes
1
answer
202
views
Constraints 'exactly/at most one non-zero element' without binary variables
In a much larger MINLP problem, I have set of variables $\{a_{ij}\}_{m,n}$, such that $0 \leq a_{ij} \leq 1 $ for all $i$, $j$, which I could think of as a matrix, for which I have two requirements:
...
- 23
0
votes
1
answer
69
views
reduced system: primal-dual interior point method for nonconvex constrained problem
When solving a reduced KKT system of a nonlinear (and nonconvex) constrained program after eliminating slack and dual variables, how do we actually take the next step in a primal-dual method?
For ...
- 325
3
votes
1
answer
292
views
Obtaining a feasible solution for underdetermined system of linear equations satisfying inequality constraints
I would like to obtain a feasible solution for an under-determined system of linear equations,
$$Ax=b$$
where, $A \in \mathbb{R}^{7\times9}, \, x \in \mathbb{R}^{9\times1}\text{and } b\in\mathbb{R}^...
2
votes
0
answers
59
views
Nonlinear Sylvester-Like Equation
Maybe you can point me to some results already developed for this.
I have to solve for $X$ the following "Sylvester-like" equation:
$$ AX - XB = F(X)$$
where $A\in\mathbb{R}^{a\times n}$, $B\in\...
- 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 ...
- 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 ...
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 ...
- 55
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 ...
- 757