Questions tagged [constrained-optimization]

Questions about optimization problems subject to additional constraints.

Filter by
Sorted by
Tagged with
3 votes
0 answers
62 views

Iterative Solvers for Linear Least Squares with Integer Constraints

The classical linear least squares problem reads $\min_{x\in\mathbb{R}^n}\|Ax-b\|^2_2$ and its solutions satisfy the normal equations $A^{\top}Ax = A^{\top}b$. A standard approach to solve the latter ...
lightxbulb's user avatar
  • 2,122
0 votes
2 answers
101 views

BFGS Constrained Optimization Failure Due to Precision Loss

I am trying to optimize the following objective function according to some constraints. However, the optimization fails at the first iteration with the message that the desired error was not ...
user47212's user avatar
0 votes
0 answers
32 views

How conservation of momentum is ensured in (Projected) Gauss-Seidel constrain solver

I'm developing molecular dynamics where my time-step is limited by stiffness of the bonds. I trying to get inspiration from game-engines, where they solve similar problem (hard bond constrains). These ...
Prokop Hapala's user avatar
0 votes
0 answers
38 views

Methods for delaying the "break" in non-linear least squares optimisation when the step size gets too small?

I am using the Levenberg-Marquardt method for calibration purposes. Typically, the RMSE of my calibration looks like: I want to break the algorithm when the algorithm step-updates start to slow down, ...
THAT'S MY QUANT MY QUANTITATIV's user avatar
1 vote
0 answers
31 views

Constraints involving max in ILP

Consider $n$ apps and $m$ transactions. $x_{ij}$ is a binary variable, it takes 0 or 1. $x_{ij}$ takes 1 if $i$th app is used for $j$th transaction, else 0. min $\sum_{i=1}^{n}\sum_{j=1}^{m} x_{ij}$ ...
Charlie's user avatar
  • 11
5 votes
1 answer
388 views

The nitty-gritty details of augmented Lagrangian methods

I am trying to implement (constrained) minimization of a certain function with the augmented Lagrangian method. Where can I find a reference that discusses in detail the good practices for the various ...
Federico Poloni's user avatar
1 vote
1 answer
44 views

Name this optimum-within-convex-hull algorithm: State is a convex combination of hull vertices; Nonnegativity ensured by reparameterization

I'm looking for the "official" name(s) for a procedure for optimizing a convex loss function over a convex subset. This seems to be a default/naïve algorithm that folks come up with before ...
MRule's user avatar
  • 153
1 vote
0 answers
39 views

Find a minium value of a function with discrete parameters, but some combinations are invalid

I'm not a mathematician, so sorry if I miss some obvious stuff. I'm trying to develop a bot for StarCraft 2, in particular the army control for it. For every army of the enemy, I want to find the ...
Ilya Peterov's user avatar
1 vote
0 answers
51 views

Beyond the LP relaxation of binary least squares

I have a binary quadratic program with a convex objective function, of the form, \begin{align} \text{minimize}\;\;& x^tAx+b^tx\\ \text{subject to}\;\;& x_i\in\{0,1\} \end{align} where $A$ is ...
Set's user avatar
  • 503
3 votes
0 answers
106 views

Implementation of the roller constraint

What could be the best way to implement the roller constraint in finite element code, i.e. constraint of the type $$\mathbf{u} \cdot \mathbf{n} = 0$$ I plan to enforce it in the weak sense by ...
kstn's user avatar
  • 241
1 vote
2 answers
200 views

Optimization Problem with Array Index as decision variable

I am trying to formulate an optimization problem where the decision variable is an index of the input array as part of the formulation. For example, I have the following term (this is simplified): $A[...
Kasparov92's user avatar
2 votes
1 answer
153 views

Numerical Simulation of a Quadratic MIP with a highly rational term

I am interested in solving the following minimization problem: $$ \begin{array}{cl} \displaystyle\min_{x,y}&\displaystyle\frac{1}{K}\sum_{i=1}^{K}\left(\frac{x_{i}}{y_{i}}-\frac{X}{Y}\right)^{2} \\...
SPARSE's user avatar
  • 169
1 vote
1 answer
115 views

Possible bug with scipy.optimize SHGO sobol: TypeError: <lambda>() takes 1 positional argument but 3 were given

I have been trying to perform some global optimization with SciPy optimizer SHGO and I've had issues with the sampling method 'sobol'. Specifically, I get an error ...
Sasche's user avatar
  • 31
2 votes
0 answers
98 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 $...
ximeng fan's user avatar
2 votes
2 answers
1k views

Why does `scipy.optimize.minimize(...)` fail with this toy constrained minimisation case?

I'm learning scipy.optimize.minimize. I thought of a simple function to see how it works: $$f(x) = x$$ With the goal to minimise $f(x)$, subject to the constraint ...
caveman's user avatar
  • 123
0 votes
0 answers
19 views

Toggling Constraints in Mixed Integer Programming

Are there MIP solvers that allow certain constraints to be toggled based on the value of a binary variable? My current situation is that I'm approximating the desired behavior by using constraints of ...
ai1013's user avatar
  • 1
1 vote
0 answers
47 views

Vehicle passenger assignment with capacity constraint

Problem Background I'm trying to find a solution to the following passenger matching problem: The network is represented by graph $G=(V,E)$. $V$ is the set of nodes/stations. $p_{ij}$ is the profit of ...
Corey's user avatar
  • 11
3 votes
1 answer
317 views

What problems does softmax() solve and when should I think of using it - in simple terms

I just for the first time saw the function softmax() in this SO answer to How do I use a minimization function in scipy with constraints and was intrigued. Another way of weighting variables where ...
uhoh's user avatar
  • 1,048
0 votes
1 answer
59 views

KKT conditions calculation for bound constrained steepest descent topology optimization

How could one calculate the KKT conditions in the case of bound-constrained optimization? In the general sense, given an objective function $J$ and design variables $x \in \mathcal{R}^n$, we consider ...
boutsitron's user avatar
0 votes
2 answers
182 views

Minimize ||AX - Y|| for a matrix A that lies in a special orthogonal group

Let $X$ and $Y$ be two given $k\times n$ real matrices. If $A$ is a $k\times k$ real matrix then $AX - Y$ is a $k\times n$ real matrix. Applying the Frobenius norm $\| AX - Y \|$, we get a non-...
David Epstein's user avatar
0 votes
0 answers
27 views

How to obtain the unitary operator to get specific partial trace using searching methods?

Is there a unitary $U_{AB}$ such that, for any density operator $\rho$, we have $${\rm {Tr}}_A \left[U_{AB} \left(\frac{I_A}{2} \otimes \rho_B\right)U_{AB}^{\dagger}\right]= \frac{\rho_B}{2}+\frac{I_B}...
Michael.Andy's user avatar
-1 votes
1 answer
98 views

what is this general form of an optimization problem (Structural) representing?

I am currently reading this article by Sigmund. Sigmund, O., Maute, K. Topology optimization approaches. Struct Multidisc Optim 48, 1031–1055 (2013). https://doi.org/10.1007/s00158-013-0978-6 I ...
Savakar Rohan's user avatar
6 votes
1 answer
221 views

Minimum distance from point to surface

I’m looking for code that is well-suited to solving a fairly simple minimization problem: I have a reference point $\mathbf p$ in 3D space, and I want to minimize $\|\mathbf x - \mathbf p\|^2$ subject ...
bubba's user avatar
  • 119
3 votes
2 answers
811 views

Why slack variables for inequality constraints?

When solving constraint optimization problems with (primal dual) interior points methods, I often read (e.g. on slide 17) that one should not use the inequality constraints $g(x)\leq 0$ directly, but ...
Manuel Schmidt's user avatar
2 votes
1 answer
113 views

Objective function for PDE-constrained boundary control problem in cylindrical coordinates

I'm interested in solving a boundary control problem for an axisymmetric diffusion problem where diffusive fluxes only appear radially. The corresponding problem for a uni-dimensional slab can be ...
IPribec's user avatar
  • 607
1 vote
0 answers
254 views

SLSQP solver scipy with linear subset constraints

I have been trying to solve a least squares problem of the following form: $$ \begin{equation} \min_{\vec{x}} \frac{1}{2} \lVert f(\vec{x}) - f_{\text{target}} \rVert_{2}^2 + \alpha\Big( \frac{1-\rho}{...
bfg's user avatar
  • 11
0 votes
1 answer
91 views

How are topology optimizations validated?

How are topology optimizations validated? I've been confused. Doesn't this mean that each of such design (e.g. N=100) would still need to be validated empirically or is there something that allows one ...
mavavilj's user avatar
  • 427
1 vote
0 answers
103 views

Using absolute error as the cost function

This is related to my previous post Minimize distance between curves. I have a dataset with values of multiple curves. An example plot is shown below. I want to scale the curves (move up/down) so that ...
Natasha's user avatar
  • 421
5 votes
1 answer
91 views

Software for Feasibility Problems

I face a feasibility problem of type $$ c_i(\boldsymbol x) \leq 0, i = 1, \dots, \mathcal{I} \\ c_e(\boldsymbol x) = 0, e = 1, \dots, \mathcal{E} $$ where $\mathcal{I} + \mathcal{E} \gg \text{dim}(\...
Dan Doe's user avatar
  • 1,083
1 vote
1 answer
78 views

Optimization software for real-valued functions of complex arguments

I am interested in an optimization problem of the form $$\min_{\boldsymbol z} \max_j \vert f_j(\boldsymbol z) \vert = \min_{\boldsymbol z} \Vert f_j(\boldsymbol z) \Vert_\infty. $$ Here, the ...
Dan Doe's user avatar
  • 1,083
-1 votes
1 answer
79 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 ...
Eugenio Monari's user avatar
0 votes
0 answers
43 views

Reformulate a problem with concave objective function into a QP

I would like to convert this problem into a QP (Quadratic program). $$\text{Maximize } \sum_{k=1}^{K}\sum_{n=1}^{N}log2(1+p_{kn}b_{kn})\\ \text{subject to } \sum_{k=1}^{K}\sum_{n=1}^{N}p_{kn}\leq P_{0}...
amhen's user avatar
  • 1
0 votes
1 answer
141 views

Efficiently solving SDP relaxation of an integer quadratic program

I have an integer quadratic program of the form, \begin{align} \underset{x}{\max}&\;\;\|Ax-b\|_2^2\\ \text{subject to}&\;\;x\in{\bf Z}\geq0 \end{align} I'm currently using the (admittedly ...
Set's user avatar
  • 503
0 votes
0 answers
815 views

optimization problem with L2-norm constraint

I am currently trying to solve a regression problem, which leads me to an optimization problem. Say that we have measured data ($\hat{S}(\omega)\in \mathbb{C}^{N\times N}$), and each entry of this ...
Hector's user avatar
  • 1
0 votes
0 answers
46 views

The condtion for Augmented Langrangian Multiplier

I am currently learning the usage of Augmented Lagrangian Multiplier to achieve my equality constraint. I have learnt from the https://en.wikipedia.org/wiki/Augmented_Lagrangian_method that I have two ...
Kevin Choon Liang Yew's user avatar
2 votes
0 answers
150 views

How is ADMM Separable?

I'm learning about ADMM by reading Boyd's paper Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers. The paper says that ADMM is an improvement over ...
user7652576's user avatar
2 votes
1 answer
119 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 \\ ...
Reda's user avatar
  • 121
0 votes
1 answer
437 views

Why is a elementwise max not DCP?

I am trying to formulate a convex optimization problem using CVXPY. Everything works, except a constraint that does not seem to follow DCP rules. Let $D \in \Bbb R^n$ be a decision variable and let $Q$...
Sahil Gupta's user avatar
2 votes
0 answers
104 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 ...
Bobbybobbobbo's user avatar
2 votes
1 answer
1k views

Python solvers for MINLP in Pyomo in Google Colab

I am looking for a MINLP solver that works with Pyomo models which can be used in the Google Colab environment. I have already found MindtPy but it doesn't work in google colab.
hosseinxj0152's user avatar
3 votes
0 answers
80 views

Sufficient condition for real roots of a polynomial of order $n>5$ with arbitrary real coefficients

I ask for help in solving the problem. I am developing an optimization program that selects the coefficients of a polynomial of order $n> 5$ so that all its zeros are just real numbers. And I ...
dtn's user avatar
  • 131
1 vote
0 answers
116 views

How to constrain the every optimized vector component to be nonnegative?

I am building a gradient descent model based on portfolio optimization. Currently, I have finished the model and am able to run it smoothly without any problem. However, there's one issue that I ...
Kevin Choon Liang Yew's user avatar
0 votes
1 answer
68 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 ...
Israa Ahmed's user avatar
6 votes
1 answer
241 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 ...
tjufan's user avatar
  • 81
2 votes
0 answers
128 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 ...
Bruno's user avatar
  • 21
1 vote
1 answer
90 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 ...
Tim Kuipers's user avatar
1 vote
0 answers
38 views

constrained zero-sum two person game

Finding the saddle point of a constrained zero-sum two-person game is equivalent to a resolution of primal-dual programs (with bi-linear objective function). I am looking for a free solver to compute ...
azra's user avatar
  • 11
1 vote
0 answers
87 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 ...
Bruce Lee Jun Fan's user avatar
0 votes
1 answer
113 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 ...
Max K's user avatar
  • 13
0 votes
1 answer
167 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 ...
Artermi's user avatar
  • 11

1
2 3 4 5 6