Questions tagged [constrained-optimization]

Questions about optimization problems subject to additional constraints.

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0answers
22 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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0answers
25 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
35 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
36 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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1answer
63 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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1answer
230 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 ...
6
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1answer
145 views

How to solve a 4th order nonnegative LASSO problem?

I need to solve the following 4th order nonnegative LASSO problem: $$ \min_{x \geq 0} \quad || |Ax|^2 - b ||^2 + \lambda ||x||_1 $$ where $|\cdot|^2$ denotes element-wise squared. $A$ is small size (e....
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1answer
84 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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39 views

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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4answers
1k views

Which C++ Multi-objective Optimization libraries allows the addition of custom problems and custom algorithms?

I'm working on a custom discrete and constrained multi-objective optimization problem and I'd like to know which libraries or platforms that implement algorithms like ...
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0answers
44 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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32 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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1answer
99 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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1answer
58 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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2answers
99 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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0answers
47 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
21 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
73 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
34 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 ...
4
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1answer
102 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
139 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
129 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
107 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
37 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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1answer
176 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 ...
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0answers
43 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, ...
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2answers
174 views

Is this a knapsack problem?

I have a set of $K$ keywords. Each of this keywords can have set of bids from $1\$,\dots,N\$$. For each bid for a keyword, it will get a specific amount of clicks and a specific cost. Clicks and Cost ...
2
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1answer
66 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
58 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
122 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
283 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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1answer
62 views

Analytic formula for $\arg\max_{\|z\|_\infty \le 1}z^T A z$, where $A=uu^T+vv^T$

Let $u$ and $v$ be column vectors of size $n \gg 1$ (not both zero), and consider the matrix $A:=uu^T+vv^T$ Question What is an analytic formula for $\arg\max_{\|z\|_\infty \le 1}z^TAz=\arg\max_{\|z\...
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0answers
69 views

Ramp least squares estimation

With some given $s$ value, let \begin{equation} \begin{aligned} h(\beta)&=\min(\sum_{i=1}^n(Y_i - X_i\beta)^2, s)\\ &=\sum_{i=1}^n(Y_i - X_i\beta)^2-\max(0, \sum_{i=1}^n(Y_i - X_i\beta)...
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3answers
182 views

Maximize a function of an orthogonal matrix

I'm trying to write up a small code that, given a set of normal vibrational modes for a molecule, will convert them to localized vibrational modes. To do this I'm following the procedure from J. Chem. ...
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0answers
16 views

Long AMPL model preparation time

We deal with a large-scale linear optimization problem (~50000 variables and ~4000000 constraints). We use AMPL Studio modeling environment for problem modeling and then calling linear solver (CPLEX, ...
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0answers
36 views

Minimizing a polynomial with millions of monomials

I need to minimize a single polynomial $P(x_1,x_2,...,x_n)$ with the constraint that for each $i$, $0\leq x_i \leq 1$. The number of variables in my practical problem is at most $50$. The degree is at ...
3
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0answers
28 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 ...
1
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1answer
53 views

Vehicle Route assignment with capacity constraint

Problem Background I'm trying to find a solution/model to the following problem: Let's consider a cellular network (mobile network, ie., hexagonal cells) denoted $N$ composed of $|N|$ cells. Each ...
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0answers
22 views

Sequence planning with 3 machines

together! First of all, I have to mention that because of my background as an Industrial Engineer, I have limited abilities in mathematics, but am disciplined enough to expand myself from ...
1
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1answer
57 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 ...
2
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1answer
346 views

Simultaneously maximize and minimize

I am virtually new to optimization (saw it years ago in a very shallow course) and now I came across a problem that I believe would require from it. The problem is I don't know exactly how to proceed. ...
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2answers
140 views

Solving a system of polynomial equations with multiple variables

I have a system of equations of the form: $$ l_i^T l_j \cdot m_i^T m_j - m_i^T R l_j \cdot l_i R^T m_j = 0$$ where $R \in \mathbb{R}^{3\times3}$ is an unknown rotation matrix. $l_i, l_j, m_i, m_j \in ...
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1answer
237 views

How to create an optimal pizza delivery plan and how to visualize it

This question is quite open, and the actual problem comes from something you would probably consider an everyday niche (something you'd probably take for granted without really thinking about it). ...
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0answers
48 views

Constraint solver vs Bayesian optimizer for fast discontinuous processes

I have a complex domain-specific process that accepts inputs: 10-500 inputs, where each input is of type: enum: choice between multiple string or numeric values int: integers float: floating point ...
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0answers
42 views

Optimization (best input variables search) for a non-smooth non-linear unknown function

I am trying to optimize a system that monitors and advises a user multiple times over a certain period of time depending on changing outside factors. The systems behavior can be altered by 5 ...
5
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1answer
544 views

Optimization of a blackbox function with an equality constraint?

I believe this would be an interesting problem. I have a blackbox function which can take 2-60 input variables $(X_1,X_2,...X_n)$ which are to be optimized. I'm calling this objective function as a ...
2
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1answer
80 views

How to add extra constraints to a linear system for probabilities?

Background: I have an equation which looks like as follows: $W \times P = R$ $$\left[\begin{array} &{1}&{0}&{0}&-\frac{w_{1}}{w_{o1}} &\dots &{0} &-\frac{w_{1}}{w_{0} } \...
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0answers
70 views

Fast approximate solver for vehicle routing problem

I need to solve capacitated asymmetrical vehicle routing problem with time windows on ~30k points. Time limits for calculations are 2 hours. I've tried using Clarke and Wright savings algorithm, it is ...
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0answers
74 views

Find a vector B that minimizes |W-A*B|

I want to find a candidate vector $B$ that $$\min|(W - A_i * B_i)|$$ $$ a_i > 0,\ A_i=\{a_0,...,a_i\},\ B_i=\{-1,0,1\}^i$$ For example, given $$W = 0.6,\quad A_4 = [0.1, 0.2, 0.4, 0.7] $$ one ...
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0answers
238 views

Solving a non-convex optimization problem using fmincon

I am trying to solve a non-convex optimization problem using fmincon(). At each iteration, I am iteratively looking for the optimum value and when the termination ...

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