Nonlinear programming is the constrained optimization (minimization, maximization) of nonlinear functions.

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0,1 binary polynomial programming

Is there a mathematical optimization branch that explicitly tries to optimize this (type) problem? $$\eqalign{ & \min \cr & \sum\limits_{i = 1}^N {(J*s[i] + {J_1}*s[i]*s[i + 1] + ...
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Generating start point in a systematic manner for fmincon

I'm trying to generate start points for my optimization problem in Matlab. At this point Im not worried about feasibility but only a fast way to generate the points from which I could test the ...
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Generating Hessian of the Lagrangian with dynamic number of nonlinear constraints in Fmincon

I'm using interior point algorithm for solving a nonlinear optimization problem and want to provide Hessian of the Lagrangian as part of fmincon to speed up the process (running couple of thousand ...
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80 views

A separable nonnegative quadratic program

I have spent quite some time trying to solve the following quadratic program: $$\min \sum_{i=1}^n (\frac{1}{2}x_i^TQx_i+c_i^Tx_i), \quad \mathrm{s.t. } \quad x_i\ge 0 \quad \forall i,$$ where $n$ is ...
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Why is SQP better than Augmented Lagrangian for nonlinear programming?

In the technical report on Galahad[1], the authors state, in the context of general nonlinear programming problems, To our minds, there had never really been much doubt that SQP [sequential ...
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38 views

Marginal values for non linear optimisation using SNOPT

I am currently solving a Non Linear modell in GAMS and I am interested in a sensitivity analysis of the results. When working with a linear program I am able to look at the marginal values for the ...
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101 views

CPLEX claims to have solved QP minimisation but solution is not optimal

I am trying to solve a small QP problem in CPLEX. The problem has several linear constraints. The optimiser runs and finds a solution which satisfies these constraints and CPLEX returns a success ...
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157 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 $A=A^T, B_i=B_i^T(\forall i\in\mathbb{N}) \in \mathbb{R}^{n\times n}, \text{rank}(A)=n,$ ...
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68 views

Optimization for differential and nonlinear system [closed]

I want to minimize a cost function for a differential-nonlinear system (dynamic). Is it possible to use this software? How can I do it? Best regards, Haniye
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2answers
593 views

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 [1]? [2] talks about it, ...
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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?
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How to solve nonlinear optimization with constraints that have singular jacobian

I'm solving a nonlinear constrained optimization with constraint of following form: $$\mathbf{A}^T\mathbf{A}-\mathbf{I}=\mathbf{0}, \mathbf{B}^T\mathbf{B}-\mathbf{I}=\mathbf{0}$$ where $\mathbf{A}$ ...
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90 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 ...
4
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1answer
132 views

constrained minimization in N dimensions

I am looking to create an algorithm to minimize an N dimensional problem. I am unsure how to write it in its generic form, so I will show it in 1, 2 and 3 dimensions Minimize $ \sum_{i} x_i\left [ ...
3
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1answer
123 views

Excluding roots from a system of nonlinear equations

I have a system of nonlinear equations of which I know it has a single root I am interested in, and has a continuum of roots I am not interested in. I am currently using Newton with line-searching in ...
2
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100 views

Some questions about MINPACK usage and messages

I am trying to use the nonlinear fitting routines of MINPACK for fitting a rather complicated equation of state to a set of experimental data. A subset of the data is fitted fairly well to a ...
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2answers
359 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 $g_i(q)$ ...
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358 views

Intuitive motivation for BFGS update

I am teaching a numerical analysis survey class and am seeking motivation for the BFGS method for students with limited background/intuition in optimization! While I don't have time to prove ...
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75 views

Is it possible to write the objective function as piecewise defined function using AIMMS or AMPL programming language in optimization problem

I would like to do a nonlinear programming problem so I need to write a piecewise linear function, but I don´t know how to do this in AIMMS or using AMPL programming language . Thanks for any help!
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What is the efficient way to solve this nonlinear programming problem

The objective function are kinds of indication function: f(x)=1, if x=1, f(x)=0, otherwise, Objective function is : max f(x1)+f(x2)+...f(xk) The constraint condition are linear, and it may be ...
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379 views

How to solve a Rayleigh-quotient-like minimization with inequality constraints

What I am trying to solve is the following Rayleigh-quotient-like minimization: \begin{eqnarray} \begin{split} (P_0)\quad\min_x \frac{\left( Ax - b\right)^\top \left( Ax - b\right)}{x^\top x}\\ s.t. ...
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Which non-linear conjugate gradient possess finite termination property

There are many variants of non-linear conjugate gradient method available ( Flatcher-Reeves, Polak-Rebiere, Dai-Yuan). In case of minimization of quadratic function when first search direction is ...
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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 ...
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Scaling of optimisation function in non-linear least squares problem

Suppose I am minimizing the following function: $$g(\alpha)=\sum_{i=1}^n(y_i-f(x_i,\alpha))^2,$$ where $y_i$ and $x_i$ are data, $f$ is a known non-linear function and $\alpha$ parameter (of ...
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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?
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nonlinear programming with support constraint

I want to solve a nonlinear optimization problem $$\underset{\mathbf{x}\in \mathbb{R}^n}{\operatorname{argmin}} f(\mathbf{x})$$ subject to a support constraint $$\mathbf{x}=[x_1,\cdots,x_n]^T, \quad ...
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647 views

parameters estimation

I have to estimate a parameter (K), but I don't know how I can do it. I think by a regression model (minimum least square?), but I'm not sure. The system is: ...
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30 views

Polynomial solvability [duplicate]

Consider the following optimization problem: Min$_{x}$ $\qquad \sum_{(i,j,t,s)\in I_r}||x_ix_j-x_tx_s||^2$ S.t.: $\qquad x\in \mathcal{C} ;$ where $x=(x_1,x_2,...x_n)$ and $\quad x_j\geq 0\;\; ...
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94 views

Feasibility checking

Consider the following optimization problem: $Min\;\;\; CX$ $AX\geq b$ $x_ix_j= x_s x_t\;\;\; i\neq j \neq s\neq t$ $x_j\geq 0;$ Where $A$ is the adjacency matrix and $C$ is a constant vector. ...
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116 views

Semidefinite programming

I have a convex optimization problem that is essentially a linear objective function over some linear constraints and also a semidefinite matrix in the following form: $ M= \left[ ...
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Nonlinear bad constraints

I have an optimization problem with linear objective function. The constraints are in two different groups. The first set of constraints are linear while the second set is nonlinear. The nonlinear ...
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Levenberg optimizer halts quickly when given more variables, or fewer constraints

I'm using the g2o C++ optimization library to refine a GPS trajectory using accelerometer data. The program uses a Levenberg-Marquardt optimizer over data points representing the position and ...
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nonlinear conjugate gradient for multivariable functions

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: ...
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C++ library for nonlinear constrained minimization

I am currently trying to solve nonlinear constrained minimization problem as implemented in matlab "fmincon" function. My expectations are, minimize(fun1,x0,uB,lB,fun2) where x0 is initial state, fun1 ...
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Is there a nonlinear solver similar to CGNR evaluating only $A^TAx$?

First of all, I am quite new to this field and I excuse myself in advance for any stupid content in this question. In the field of compressed sensing or deblurring I have a nonlinear optimization ...
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1answer
126 views

Test set non linear solver

what is your preferred test set to test quality of non linear solver? this could be set of data, model and results obtained with some benchmark solver, or simply a panel of test functions that could ...
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340 views

Line search for Newton method

If we want to solve nonlinear minimization problem $$\min_{x} f(x),$$ making least-squares assumption and using Gauss-Newton method so that at k$th$ iteration we have: $$J_k^T J_k p_k = - J_k^T ...
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What is too big for standard linear algebra/optimization methods?

Different numerical linear algebra and numerical optimization methods have different size regimes where they're a 'good idea', in addition to their own properties. For example, for very large ...
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570 views

Minimizing a quadratic function with nonlinear constraints

what would be good methods (and/or software packages) to try for solving a problem minimizing a quadratic function $f(x) = \sum_{i=1}^N{(x_i - y_i)^2}$, s.t. $0 \leq x_i \leq 1$, and there are more ...
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391 views

Decomposition methods for solving large optimization problems

I was wondering if anybody had any suggestions for texts or survey articles on decomposition methods (e.g. primal, dual, Dantzig–Wolfe decompositions) for solving large mathematical programming ...
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Is it possible to run a Solver Foundation solver against a model containing linear and non-linear elements?

This is a follow up question to one I made previously about non-linear equations and ranged real numbers in Solver Foundation. I acknowledge that where possible, rewriting a problem that is ...
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Efficient principal pivots

It was suggested I should try posting this question here from Mathematics Background I'm working on a numerical linear algebra package in C#. I'm trying to implement a variety of "principal ...
5
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1answer
233 views

Reducing degeneracy in constrained (convex) optimization problem

DISCLAIMER: I've edited the question repeatedly for clarity and to target the most relevant answer. I have the following general problem $$ \min \|h_1\cdot h_2\|^2 $$ such that $$\|g_1\wedge ...
3
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1answer
155 views

Can BFGS be used to minimise several functions at once?

I have multiple objective functions which are related to several parameters. I want to minimise more than one objective functions using several parameters. Is it even possible using BFGS? When I used ...
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867 views

Software package for constrained optimization?

I am looking to solve a constrained optimization problem where I know the bounds on some of the variables (specifically a boxed constraint). $$ \arg \min_u f(u,x) $$ subject to $$ c(u,x) = 0 $$ $$ ...
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best way to optimize a function with linear/non-linear parameters

I am trying to fit some raw data using a function of the form $f(r) = \sum_{i=1}^{K} d_kS_k(n_k,\alpha_k,r)$ where $S_k(n_k,\alpha_k,r) = \frac{\alpha_k ^{n_k+3}}{(n_k+2)!}r^{n_k}\exp(-\alpha_kr)$ ...
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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 ...