Computational Science Stack Exchange
Computational Science Stack Exchange

Questions tagged [constrained-optimization]

Questions about optimization problems subject to additional constraints.

300 questions
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Line search for constrained optimization

I have a nonlinear inequality constrained optimization problem of the form $$\begin{array}{cc} \min & f(x) \\ \textrm{s.t.} & g(x) \ge 0 \end{array}$$ where $x \in \mathbb{R}^n$, $f : \mathbb{R}^n \to \mathbb{R}$, $g : \mathbb{R}^n \to…
Geoffrey Irving
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optimization subject to disjunction of inequality constraints

I want to solve $$\min_x f(x)\qquad \textrm{s.t.}\qquad g_i(x) \geq 0\ \ \textrm{or}\ \ h_i(x) \geq 0$$ for $i=1,\ldots,m$. Clearly if the inequality constraints split the feasible set into $2^m$ disconnected components, there is no hope for an…
user168715
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Derivative-free nonlinear optimization of discrete objective function with linear constraints (simplex)

I am trying to optimize a constrained-problem with a discrete, non-linear objective function. Evaluating this function is also fairly expensive. Nevertheless, despite the above two factors, I hope, that it can still be solved efficiently, since the…
air
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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 $s_i$ are the scalars. So the matrix $A$ should have the…
jakeoung
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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 competencies. I am working in a production plant in the…
Aaron
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What are the novel MOOP method?

As you know, the multi-objective optimization methods are developing so fast, i.e.,epsilon constraints. I have a problem that I want to apply the most recent MOOP method for it. Please tell me the recent methods for solving multi-objective…
Masan
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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 GLPKSolverMIP() can someone explain to me the difference in these two optimization strategies? Both of these optimizers are…
Austin
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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, C[1,1]: x-coordinate of the first circle C[1,2]: y-coordinate of the…
jakeoung
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What are the numerical properties to consider between Augmented Lagrangian and the Penalty Method?

I'm interested in (locally) minimizing a smooth nonconvex objective function: $$ f(\textbf{x}_1, \textbf{y}_1,\cdots, \textbf{x}_n, \textbf{y}_n)=\sum_{i=1}^ng(\textbf{x}_i, \textbf{y}_i) $$ Subject to $\textbf{y}_{i+1}=\textbf{h}(\textbf{x}_i,…
VF1
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Minimization of least square function together with a nonlinear function

I have the linear underdetermined system $$Ax=b$$ and I need to find $x$ constrained by the maximization of a score function $g(x)$. I could find the minimum of a function like $$|Ax-b|^2+1/g(x)$$ but I wanted to know if there exists a canonical way…
N74
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Allocation under constraint (optimization ?)

I have a problem of allocating x between p entities, each entity has a constant $\rho_i$ such that the allocated part should be proportionnal. Without loss of generality we can divide the ressources by x and normalise the $\rho_i$ by…
Lucas Morin
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Picking highest value non-adjacent groups within a set

Imagine you are given 20 random numbers in a row. The original order must be maintained. From this set you can choose 2 groups of 3 numbers each. The position of these groups must be separated by at least 4 numbers. The goal is to maximise the sum…
KieranPC
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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 the following optimization…
boutsitron
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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 model where there are only a finite number of…
Emil
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SQP for Quadratic Cost function optimization subject to linear & nonlinear Constraints

Is it possible to solve a quadratic cost function which is subject to both nonlinear (quadratic) & linear constriants by SQP methods? If not, what is the best iterative solution for this kind of problem? Thanks
M.Nitro
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