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

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Find $\min \sum_{1\le i\le n} x_i\mathbf{z}^T\mathbf{A}\mathbf{y}_i +\mathbf{b}^T\mathbf{x} +\cdots$

I have been stuck at this problem for a while :( Given $\mathbf{A}\in\mathbb{R}^{p\times p}, \mathbf{A}\ge 0,\mathbf{A} \text{ symmetric}, \mathbf{b}\in\mathbb{R}^n,\mathbf{c}_i\in\mathbb{R}^p\forall ...
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comparing different practical convex optimization algorithms

I am trying to implement limited memory bundle method on piece-wise linear convex optimization problem (with dimension=5000) in c++, however, it seems limited memory bundle method code is not ...
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98 views

Dealing with errors in non-linear least square problem

I am currently working with a optimization problem involving a non-linear least square problem. I have chosen to use lsqnonlin in Matlab. What follows is a ...
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1answer
38 views

Solving nonlinear optimization problem with combinational constraints

I have to minimize a nonlinear objective function $f(x_0, x_1, x_2, x_3, x_4, x_5)$ with 6 variables. The constraints governing these these variables are a mix of nonlinear inequality constraints, ...
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1answer
52 views

Is there general algorithms to solve such 3D cutting problems?

Suppose a cuboid $\mathbb{A}$ has $L$,$M$ and $N$ as its length, width and height respectively, where $L\ge{M}\ge{N}>0$; Now we want to cut $\mathbb{A}$ into smaller cuboids with length $x$, width ...
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1answer
64 views

Constraint containing 'max' in linear program unnecessary?

The problem that I'm trying to solve is as follows. A server has at its disposal a pool of video encoders (each encoder has different settings and causes a different load on the server) that can be ...
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1answer
44 views

Mac/Xcode/C++ connect with GAMS

Basically, I failed to trying to implement individual global MINLP solvers (alphaBB, ANTIGONE, BARON, Couenne, LindoAPI, and SCIP) in C++/Xcode/Mac system. On the other hand, I realize that GAMS ...
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55 views

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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107 views

Find $\min x^TAy$ subject to $1^Tx=1^Ty=1,x\ge 0,y\ge 0$

In the following problem, $A$ is a given $\mathbb{R}^{m\times n}$ matrix: \begin{align} \mbox{minimize}\quad & x^TAy \\ \mbox{subject to}\quad & 1^Tx=1^Ty=1, \\ & x\ge 0,y\ge 0. ...
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63 views

Piecewise linear optimization with resource allocation constraints

I have this problem: \begin{align} \min_{\mathbf{w}} & \sum_{i=1}^N c_i P_i(w_i)\\ s.t & \notag\\ & \sum_{i =1 }^N w_i = w \\ & 0 \leq w_i \leq w_{max},~~\forall i \in 1, ..., N ...
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96 views

Methods for Constrained Optimization Problems with Box Constraints

Consider this problem: \begin{equation} \begin{array}{ll} \text{minimize } & f(x) \\ \text{subject to } & a \leq x \leq b \end{array} \end{equation} where $a,b,x \in ...
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Large-scale nonlinear optimization problem

I want to solve a nonlinear optimization problem of the following form \begin{equation} min( \sum_i d^{x_i}c_{i})\\ 0 \leq x_{i} \leq a\\ \sum_{i} x_{i} \leq b \end{equation} $a$, $b$, $0.95 < d ...
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84 views

Solving 10000, Non-Linear, Simultaneous Equations

Could anyone let me know if there is any optimization solver that I can use to solve about 10,000 simultaneous equations (most of which are non-linear) using Python? Please also advise if it is ...
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1answer
68 views

fitting a non-linear curve

I have an equation: $\ddot{x}+(\delta+\epsilon\cos{t})x=0$ known as the Mathieu equation.The $\delta-\epsilon$ parameter space of this equation looks something like The red lines in this diagram ...
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1answer
63 views

Does the amount of correlation of model parameters matter for nonlinear optimizers?

I am using nonlinear optimizers such as BOBYQA to train a model with 10-20 parameters. It so happens that some of the parameters have high correlation. Roughly speaking, imagine that you are fitting ...
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118 views

How to solve this optimization problem with abs object function?

Helo, every one. May I ask for help about how to solve this problem. $\begin{align} & \text{max}_{x_i} \quad |\sum_{i=1}^{4} a_i x_i | \\ & s.t. \quad \sum_{i=1}^4 x_i^2=1 \end{align} $ ...
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170 views

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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104 views

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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94 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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1answer
57 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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305 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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171 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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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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1k 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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90 views

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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87 views

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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158 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 ...
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153 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 [ ...
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129 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 ...
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1answer
191 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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640 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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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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70 views

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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675 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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262 views

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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212 views

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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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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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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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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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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115 views

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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1answer
466 views

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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139 views

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 ...