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Questions tagged [constrained-optimization]

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Questions about optimization problems subject to additional constraints.

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Can line search solve linear objective with nonlinear constraints?

Consider an optimization problem of the form: $$\max_{f(x)\le K,\\0\le x\le M} c^\top x,$$ where $f(x)$ is nonlinear. Can a line search of the following form be used to solve this problem? $$ \max_{\...
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1answer
60 views

Expressing a Constraint in an optimization problem

If I have a vector of M "continuous" decision variables (say it is called x) , and if I want a constraint to express that only one of them is allowed to have a nonzero value (i.e. no more ...
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176 views

Optimization problem

In the expression: $${\underset{\Omega}{\min}\left\|\beta A\Omega^{-1}B+C\right\|_{F}^{2}}\, ,$$ $$\text{subject to tr}(\Omega)=1, \Omega \ge 0\, ,$$ where ${\Omega}$ is nonnegative and symmetric ...
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71 views

Efficient solver of a Integer programming

I am solving an Integer programming using MATLAB, yet the efficiency is low. Here is the problem: Suppose $v$ is a $N \times 1$ vector. For $v_i \in v$, $v_i \in \{0,1\}$. $D$ is a 0-1 matrix, which ...
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1answer
53 views

Overconstraining in SQP

In Sequential Quadratic Programming we use an active set of the inequality constraints and handle them as equality constraints in the quadratic subproblem. SQP is said to be able to deal with ...
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56 views

Constrained optimization for non-linear equations in octaveGNU

I have installed Optim1.6.1 package. I would like to solve a system of equations in non linear finite element analysis using constraints as u=1 at certain nodes. u=0 at certain nodes. Typically I find ...
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1answer
49 views

Variable equality constraints in SDP Problem

I'm quite new to SDP programming, hence I might not have been able to use the right search terms to find a solution. I try to reformulate an SDP problem to the original form. However a side constraint ...
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1answer
55 views

Maximum Constraints Satisfaction of Linear Programming

The question I need to solve is to maximize the satisfied constraints in linear programming. To be more specific, Suppose I have an infeasible LP problem, my goal now, is to find the maximum number of ...
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64 views

High quality constrained optimization C++ library with matrix free second order solver?

I'm working with large scale constrained optimization problem. Some of my constraints can be non linear. Currently i'm using IPOPT. Quality is good by my Hessian computation too slow. It seems that i ...
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1answer
40 views

Difference between LP optimization and GLPK optimization

I've seen two different optimizers being used, but both with a different solver. One uses PULP_CBC_CMD and the other uses ...
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1answer
71 views

Is there an overview of the runtime speed up of LP/MIP solvers throughout the years?

whenever I read papers on OR that use an LP/MIP approach, they include the time solver used, as well as the version and the year. I would like to know how much faster the same experiment would be ...
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87 views

CVXOPT intermediate step valuation stepping out of function domain of defintion

I am using CVXOPT, particularly to solve a nonlinear convex optimization problem. Either the objective function or the constraints involve some functions that are only defined in a strict subset of $\...
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65 views

L2 norm optimization problem

I have an optimization problem where i need to find an image x, that is very close to x' such that: monitor(x') is valid but monitor(x) is invalid. (output is valid when the neural network output is ...
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84 views

Finding the extrema of a transition probability function for a quantum walker on a graph

The goal Implement some Python code to find the extrema points of a function that is strongly oscillating. The background Let $G$ be a connected graph with $n$ points with Laplacian matrix $L(G)$. We ...
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1answer
193 views

SCP (Sequential Convex Programming) vs SQP (Sequential Quadratic Programming)

Can someone explain me at a high level the difference between an SCP and an SQP to solve a nonlinear (nonconvex) program? Assume my problem is something like $$\min\limits_x. \quad f(x)$$ $$s.t. \...
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51 views

Model and solve nutrition optimization problem: how to?

How to solve/assess the following problem? Given: $N$ ingredients like apples, bread etc. Mass of an ingredient $j$ is in this simplified model a sum of macro nutrients carbohydrates, proteins and ...
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133 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 ...
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1answer
163 views

How to best code a problem with scipy, cvxpy or Convex.jl with given generated data

I have a curve fitting problem of the form: $$ \textbf{y} = f(\textbf{x}, a,b,c,d) + \varepsilon $$ $$ f(x, a,b,c,d) = \frac{b}{e^{x\cdot a}+c}+d $$ with the constraint \begin{equation} \begin{aligned}...
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66 views

How applying the gradient descent method for solving a least square problem can remove the blur from an image?

I got an assignment where it asked to implement (in MATLAB) the gradient descent algorithm in order to resolve an ill posed least square problem: $$ \min_u \Vert Gu - f \Vert $$ where $u$ is the ...
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2answers
98 views

How to determine guitar tones played as early as possible?

I want to detect chords on a guitar as early as possible, but my approach with a sliding window and a filter bank seems to introduce too much lag. Would required observation time decrease by using a ...
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1answer
217 views

Good languages/packages for interior point optimization with non-linear constraints?

I'm currently using Python's scipy.optimize package to perform parameter estimation for a system of 10 ODEs. I have some observed data, and I'm trying to find the set of parameters which makes the ODE ...
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78 views

How can I deal with optimization problems that have a sum of functions of Z as a constraint when Z is the quantity to be minimized?

I have a problem where I have to minimize a certain quantity $Z$ subject to the following constraints:- $w_1 + w_2 + w_3 = 1$ $\frac{f_1(w_1*Z) + f_2(w_2 * Z) + f_3(w_3 * Z)}{Z} >= k$ where $k$ ...
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30 views

Bipartite Euclidean Matching simple to implement approximate algorithm

I am looking for a simple to implement algorithm for the bipartite euclidean matching problem (or an implementation of any practical algorithm). I am aware of Agarwal's paper, but I would like to ...
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41 views

Implementation method selection for sparse constrained linear least squares or quadratic programming

I need to slove one optimization problem of quadratic programming. The number of optimization variables is about 16,000. The constraints include equality constraints and inequality constraints. I have ...
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1answer
63 views

Constraint programming problem with conditional constraints and some unknown indicator variables

I have an interesting little problem that I believe can be formulated in terms of optimization or constraint programming. I have a few dozen variables $a$, $b$, $c$ ... and a set of constraints that ...
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1answer
117 views

Why is quadratic penalty method used for equaltiy-constrained optimization?

When one equality-constrained optimization is formulated, the method of Lagrange multiplier will be the choice for me. In Chapter 17 from the book Numerical Optimization, quadratic penalty method can ...
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276 views

Can this simple quadratic optimization problem be turned into a simple eigenvalue problem?

I'm interested in a type of problem on this form $$\min_{x} x^{T}Ax+x^{T}b \quad \text{s.t} \quad x^{T}x=1 $$ where $A$ is positive definite. As you can see, if it weren't for the $x^{T}b$ term in the ...
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Balanced constraint

In several optimization problems, we found what we called the balanced constraint(c^T • x = z ) For exp: C^T • 1 = 0 (C is a binary Matrix) Can I have an intuitive explanation about the concept and ...
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92 views

How to speed up the Mixed-Integer Quadratic Program process?

Currently, I am solving a problem in the format: M is an integer as well. The problem that troubles me is that X is a vector in {0,1} with a size of 7000. I use the solver in https://github.com/...
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36 views

What is the generalization of the resource allocation problem I'm dealing with here?

I'm dealing with a problem as follows: I have a finite set of money 𝑚 to spend over 𝑟 different raffles, and I need to spend approximately to my budget, with the goal of maximizing my probability ...
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2answers
163 views

Solve two-player game - minimize the l-infinity norm of a matrix-vector product

I have a matrix $M$ with non-negative real entries, and I would like to minimize the objective function $$\Phi(v) = \|Mv\|_\infty,$$ where $v$ is constrained to be a probability vector, i.e., $v_1+\...
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1answer
126 views

Linear system with an l1-norm constraint

I have a saddle-point system of the form \begin{equation} \begin{bmatrix} A & B \\ B^T & O \end{bmatrix}\begin{bmatrix} x\\ y \end{bmatrix} = \begin{bmatrix} f \\ \vec{0} \end{bmatrix}, \end{...
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1answer
248 views

Non-negative least squares with very small numbers

(I have asked this question on StackOverflow previously but it has been pointed to me that CSSE or MSE could be more appropriate) I have to solve a constrained optimization problem of the following ...
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55 views

Least-squares fit of explicit parabolic sheet to data points

For a given set of data points $$\{(x_i, y_i, z_i)\}$$ there exists some $$f_{ABC}(x,y)=Ax^2+Bxy+Cy^2$$ that minimizes $$\sum_i(f_{ABC}(x_i,y_i)-z_i)^2$$ $A$, $B$, and $C$ can be found quickly ...
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1answer
22 views

Python: Getting second output variable from minimizing a computationally intensive function on first outputs

I have a function in python that is quite computationally expensive to evaluate, of the form: ...
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2answers
116 views

Using MILP to place a set of primers along a genome

Define variables $p_i,u_i\in\{0,1\}^G$, for $i=1,\ldots,8$ and $G=30000$. Let $v$ be a constant vector also in $\{0,1\}^G$, with approximately 25% of its entries equal to $1$ (randomly located). Let ...
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1answer
102 views

Plotting optimum as a function of parameter in the objective

I am trying to minimize a 2d function using scipy.optimize. Specifically I want to plot the minimum value of the function fun as a function of the parameter wjk. The problem is that I cannot pass wjk ...
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2answers
114 views

How to minimize $(x-a)^2+(y-b)^2$ subject to $ \sqrt{a}+\sqrt{b}=\sqrt{2}$?

I am not sure if this is on-topic here, but I am trying. Let $x,y$ be positive real numbers. I am trying to find $$ \min_{\sqrt{a}+\sqrt{b}=\sqrt{2}}(x-a)^2+(y-b)^2$$ I tried using Mathematica for ...
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1answer
86 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 ...
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1answer
184 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} \...
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1answer
550 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 ...
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0answers
60 views

Lexicographically order matrix into a vector

I am trying to implement the algorithm contained in this article here. It is about solving a 2 and 2.5D Fredholm integral, focused on bidimensional NMR experiments. I've made significant progress, ...
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159 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 ...
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2answers
141 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 ...
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0answers
44 views

Optimization of centers and radii of circles under the non-collision constraint

I want to optimize a function w.r.t. $n$ circles parametrized by centers and radii: $$\min_{C, R} f(C,R)$$ where $C\in\mathbb R^{n \times 2}$ and $R\in\mathbb R^n$. For example, ...
4
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1answer
202 views

Underdetermined Minimum Volume Enclosing Ellipsoid

Given three vectors in $\mathbb{R}^{512}$, my task is to compute a Minimum Volume Enclosing Ellipsoid (MVEE). I have tried Kachiyan's algorithm, but it requires at least as many vectors as there are ...
2
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1answer
77 views

Optimization with the constraint of rank=1

I have the following matrix $$ A = [x_1, x_2, ..., x_n], $$ where $x_i \in \mathbb R^n$. But I know the relationship that \begin{align} x_2 = s_2 x_1 \\ x_3 = s_3 x_3 \\ ... \end{align} where $s_i$...
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1answer
130 views

Could the convex problem be tackled by CVX?

I want to solve the convex optimization as follows: \begin{align} \underset{X_1,X_2}{\min} &\ -\frac{1}{N}\sum_{i=1}^N\log\det\left(I+H_i^HX_2H_i\right)-\log\left[1+h^H(X_1+X_2)h\right]\\ &\...
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1answer
275 views

Gradient descent in constrained optimization of barrier function

This question may be too basic, but I was wondering if it is possible to implement simple methods such as gradient descent or its variations to find the minimum of barrier functions in constrained ...
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2answers
890 views

How to solve calculus of variations problems numerically?

For example, how to solve the well-known isoperimetric problem (i.e., to enclose the largest area with a fixed-length curve)? We can simplify things a bit and fix the two ends of the curve at $[a,0]$,...

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