Questions tagged [nonlinear-programming]
For questions about mathematical optimization problems involving a nonlinear objective function and/or nonlinear constraints.
189
questions
3
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0
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63
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Looking for an efficient way to solve a fractional problem (affine function over euclidean norm )
While working on optimization issues I encountered the following problem:
$$\left\{\begin{array}{ll}
{\displaystyle \sup_{z\in\mathbb{R}^{m}}} &\frac{ \langle c,z \rangle + \rho}{ \left\|B z\...
- 131
2
votes
3
answers
103
views
Linearization the product of three variables (two binary & one continuous)
Consider the following binary variable $x \in \{0,1\}$ and two continuous real variables $y,p \in \mathbb{R}$.
I am trying to model the following conditional equations as constraints:
\begin{cases}
...
- 103
1
vote
4
answers
113
views
How to perform clustering of a large number of nodes?
I have a clustering problem with around 400-500 nodes. The edge between any two nodes has a weight (between 0 and 1, 0: can be considered as there is no edge/connection between these two nodes) as ...
- 2,179
1
vote
2
answers
90
views
My barrier function is always giving a complex number
I am working on implementing the interior point method, and the barrier function always gives me a complex number. B(x) = f(x) - t * sum(ln(hi(x))). I have changed the value of 't' to see the B(x) ...
1
vote
2
answers
538
views
Non linear programming
I want to solve a large scale non linear optimization problem and there are two methods interior point method and sequential quadric programing usually used to solve non linear optimization problem. I ...
2
votes
2
answers
91
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I want to solve an optimization problem with nonlinear piecewise objective function (I tried Pyomo with "ipopt" solver but I had an error)
I want to solve an optimization problem where the objective function is the summation of nonlinear, piecewise functions in the decision variables q_i's such that when a decision variable q_i < 1, ...
- 21
2
votes
1
answer
68
views
Nonlinear fractional objective function
Could you please teach me when an optimization model with fractional terms in the objective function can be linearized or solved optimally?
I only know that if the objective function has a single ...
1
vote
2
answers
57
views
Solving single-variable fractional equation
Can anyone advise how this nonlinear equation with a single variable $x$ can be solved as a closed form?
${\left(\frac{x}{1-x}\right)}^2.{\left(\frac{x-C}{\left(1-x\right)-N}\right)}^2=H.\frac{2x-C}{2\...
2
votes
1
answer
106
views
Formulation of nonlinear nonconvex optimization problem and finding appropiate solver
Consider the notation and objective below for this sequential resource allocation problem:
Allocation channels $i \in (1, 2)$
Spend/Cost timestep i channel j: $C_{i, j}$
Total resource: $B$
Horizon: $...
3
votes
1
answer
80
views
Modelling a decision variable as an index of a (fixed) set
I'm trying to model the following MINLP problem in Pyomo.
We are trying to minimize a nonlinear objective function $f$ in $x_i \in \lbrace{0, 1, 2\rbrace}$ for $i= 1, 2, \dots, N$ and subject to a ...
- 1,001
2
votes
1
answer
91
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Implementing a MINLP problem in Pyomo: giving an infeasible solution
I'm trying to implement a MINLP problem which is described in a previous post here: How do we formulate a problem where the decision variable has an index that is also a decision variable?
The only ...
- 1,001
6
votes
3
answers
430
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How do we formulate a problem where the decision variable has an index that is also a decision variable?
I want to maximize the sum of a nonlinear function $f(.)$ w.r.t. $x$ that is convex in $x$:
$$\max \sum_{i=1}^N f(x_i), $$where $x_i$ is a continuous variable and $0 \le x_i < 1$ for $i = 1, 2, \...
- 1,001
2
votes
1
answer
162
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OR-Tools: Nonlinear constraints?
I have inherited a reasonably simple ortools-based optimizer (Python) with linear relationships that I need to non-linear-ize, and I have no idea how to do that.
The relevant part of my problem looks ...
- 121
1
vote
1
answer
122
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Formulating a continuous NLP problem with a class variable
In this minimization problem we have $N$ items, $j= 1, 2, \dots, N$ and a decision variable $x_j$ which are continuous values.
For every item, we have a nonlinear objective function $f$ in function of ...
- 1,001
5
votes
1
answer
251
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Optimize selection of metal sheets to keep in stock
I already asked this on stack overflow but just found this forum instead and figured it was more suited here. If this isn't allowed please feel free to tell me and I'll delete the post.
I am doing ...
- 53
-1
votes
2
answers
84
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How to apply smooth approximation to non-linear complementarity constraints?
$P =$
$ x, if U \geq U^{max} $
$ y, if U^{up} < U < U^{max} $
$ z, if U^{down} < U < U^{up} $
$ \alpha, if U^{min} < U < U^{down} $
$ \beta, if U \leq U^{min} $
Where $P$, and $U$ ...
2
votes
0
answers
46
views
Branching the product of binary and continuous variable in Gurobi
I have a binary variable (X) multiplying a continuous variable (Y). I know I can linearize by adding an auxiliary variable (I have that model working), but I now want to do my own branching in the ...
- 423
2
votes
1
answer
82
views
Formulate revenue maximization problem and find an appropriate solver
I am trying to maximize expected revenue over a horizon.
Consider the following function:
\begin{align}
sales(budget_1, budget_2) = \sum_te^{C_1t} * budget_1t^{saturation_1t} + e^{C_2t} * budget_2t^{...
4
votes
1
answer
160
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How to solve a "nearly" linear program
Given a positive integer $n$, a constant $k=2/3$, and $7$ variables $x_1, x_2, x_3, x_{12}, x_{13}, x_{23}, x_{123}$ (non-negative reals or integers) I would like to find:
$$\min \binom{x_1}2$$
...
- 393
2
votes
1
answer
103
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How to mathematically model this multi-objective optimization problem?
I have a system of $M$ machines and $U$ users.
Each machine has a capacity in terms of number of resources.
Let, machine $m$ has $\zeta_m$ resources.
Each user has a service demand $d_u$ and there is ...
- 2,179
3
votes
1
answer
103
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How do I pass an objective bound to Gurobi?
I have a non-convex Quadratic Programming over unite simplex set. I have a valid lower bound on the objective function (goal is minimization problem).
If I add a constraint like
$$f(x)\geq lower~bound,...
1
vote
0
answers
51
views
How to avoid complementarity constraints in continuous nonlinear program?
In my two-stage continuous NLP problem, I have a constraint in second stage:
$X_{g,k}$ = $X_{g,0} + a_{g} d_{g} $, if $X_{g,k} \in [X_g^u,X_g^l]$
$X_{g,k} = X_g^u$, if $X_{g,k} \geq X_g^u$
$X_{g,k} ...
1
vote
1
answer
56
views
An if-then-else logic whose condition is an inequality
I was hoping to get some help in modelling the following logic. I tried to solve it by "Big-M method" but failed. Thank you in advance!
$a(k,n)$ and $b(k,n)$ are known constants, $\lambda$ ...
- 33
-1
votes
1
answer
89
views
Ipopt finds a better solution if I do not eliminate the zeros in the hessian matrix ?(we eliminate the zeros by defining the structure)
I use Ipopt to solve a problem with sparse hessian and jacobian matrices.
If I provide the hessian matrix: its structure, and the non zeros elements in the hessian matrix, it will be really fast.
If I ...
- 391
0
votes
1
answer
59
views
The max_wall_time and max_cpu_time in ipopt are not working?
The max_wall_time and max_cpu_time are not working in ipopt (cyipopt).
See example:
...
- 391
0
votes
2
answers
88
views
Bellman Equation for nonlinear model
Consider the following model:
\begin{align*}
max \quad Z &= 19x_1 - 3x_1^2 + 5x_2^2 - x_2^4 + 4x_3 \\
& s.t. \quad x_1 + 3x_2 + 3x_3 \leq 7 \\
& \quad \quad \quad x_1,x_2,x_3 \geq 0
\end{...
1
vote
1
answer
164
views
Should I provide the hessian matrix, hessian structure, and Jacobian structure if I use cyipopt (IPOPT) if I am concerned about computation time?
If I use IPOPT (cyipopt) to solve nonlinear problems of large scale. It is optional to provide or not provide the hessian matrix, hessian structure, and Jacobian structure.
The question is which one ...
- 391
2
votes
0
answers
55
views
Minimizing sum of similar functions with a dependence
Consider an objective function in the form of minimization of maximization that is the sum of $N$ similar functions $f\left(x\right)\ge 0$, $\ \forall x$. The summation of all variables is constant (e....
4
votes
0
answers
73
views
How to linearize or convexify a constraint with a square root of sum of two variables?
Here is the constraint:
$$\text{Pa} + \text{Pb}=a + b \sqrt{\text{Ir}^2 +\text{Ii}^2} + c (\text{Ir}^2 +\text{Ii}^2)$$
Here $\text{Pa}, \text{Pb}, \text{Ir},$ and $\text{Ii}$ are variables. $a, b, c$ ...
1
vote
2
answers
108
views
How to formulate this NLP problem correctly?
Current status on the problem (what I've done)
I'm working on a NLP problem and I got a formulation of the problem, together with the necessary constraints, but I think it needs some adjustments to ...
- 1,001
3
votes
2
answers
170
views
Can we use continuous variables instead of binary variables in this NLP problem?
The following problem is defined with binary variables $a_{i1}, a_{i2}, a_{i3}, k_1$ and $k_2$.
Is it possible to avoid binary variables and to only work with continuous variables? How would we ought ...
- 1,001
2
votes
1
answer
44
views
Automatic Reformulation Tools For AML Programs
Are there any tools to transform programs written in an algebraic modeling language like GAMS,AMPL,... into a different formulation.
E.g. there is a quadratic constraint $\sum_j b_i b_j = N, b \in \...
- 153
3
votes
0
answers
81
views
Linearize objective function with non-linear terms
I have a problem with linear constraints but in the objective function I want to have some linear terms along with a $x^2$ term. So it is like the following:
$$\min \sum \limits _i \sum \limits _j (a[...
3
votes
1
answer
136
views
Modelling a nonlinear minimization problem with a nested function
I'm thinking about the following problem:
Suppose you have $n$ items and every item $i$ has constants $D_i, p_i$ and $c_i$.
$D_i$ is the demand for an item and $p_i$ is the price for that item.
Now $...
- 1,001
7
votes
3
answers
468
views
Profit Maximization LP and Incentives Scenarios
I wrote a profit maximization LP with inventory, component usage, production, and machine hours constraints. When I optimize the model, it solves as expected. When applied towards a business case, ...
- 83
3
votes
1
answer
89
views
Problems involve exponential equality constraints
I have a question like
Let, $\mu = (\mu_1,\ldots, \mu_K),$ given $M: K \times m$ a full rank matrix
$\min_{\mu \in \mathbb R^K} \sum^n_{i=1}\sum^K_{k=1}(y_{ik} - \mu_k)^2$ subject to $\log \mu = M\...
- 33
2
votes
1
answer
94
views
Convex Optimization, Non-negativity constraints, Interior-Point or Projected Gradient?
Assume I have the following convex optimization problem, with a convex objective function on conventional non-negativity constraints.
\begin{align}
\min_{x \geq 0} \sum_{i=1}^{I} a_{i}x_{i} - f(...
- 129
3
votes
0
answers
121
views
How to find robust counterpart of sum of logit functions?
Suppose function $\mu_i(y):\mathbb{R} \rightarrow \mathbb{R}$ is a logit function, $\mu_i(y)=1/(1+\exp(-y))$. Also, we assume that $\mathbf{x}_i\in \mathbb{R}^d$ and $\theta \in \mathbb{R}^d$. I am ...
- 2,140
3
votes
1
answer
382
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About Objective Function Manipulation
I have an objective function as follows (updated after the clarification question):
$$\max_{x∈X}\left(\sum\sum c_{ij}x_{ij}-\max_{y∈Y}\sum\sum d_{ij}x_{ij}y_{ij}\right)$$ where
$x_{ij},y_{ij}$ are ...
- 333
2
votes
1
answer
115
views
multiple solutions to a nonlinear problem in GAMS
Good afternoon, I have the following doubts
Is there a command in GAMS that lets me know when my problem has multiple optimal solutions?
Suppose my nonlinear optimization problem has multiple global ...
- 183
5
votes
3
answers
559
views
Model infeasible
What should you do when you face an infeasible solution? I have implemented the model with the dataset from the paper but found infeasible solution.
- 573
8
votes
1
answer
336
views
Solving maximization problem with linear-fractional sum
I want to solve this problem :
Maximize \begin{equation} \sum_{i=1}^{n} \frac{x_i}{a_ix_i + b_i}\end{equation} with the constraints \begin{equation}\sum_{i=1}^{n}x_i = S \ , \ x_i \geq 0 \ \forall \ ...
- 83
4
votes
1
answer
397
views
Is this a non-linear integer model?
Let's say if I have two decision variables, $f$ and $g$ respectively, where $f$ is continuous, and $g$ is binary.
If I have a constraint like this,
$$ f\cdot g \le C$$
Does this make my model ...
- 573
2
votes
1
answer
76
views
Lifting a 3rd order polynomial into a higher dimensional space
An MINLP from a paper I am reading has the following expression in its constraints:
Where from left to right:
$p_{l,s}$: continuous variable
$z_l$: binary variable
$b_l$: constant
$\Delta \theta_{l,s}...
- 103
2
votes
3
answers
269
views
Minimizing a monomial function subject to inequality constraints
Assuming an objective function is a multivariable polynomial with real coefficients, in variables {x1, x2, ..., xn} with all exponents no larger than 1, and with linear inequalities on the variables, ...
0
votes
0
answers
42
views
How do i model this problem as an stochastic optimization problem
Consider the following optimization problem:
$$\begin{align}
\max_{inv1t, inv2t} \sum_{t=t}^{t=t+H} r(inv1t, inv2t, & independent \; variables) \\
\mbox{s.t.} \sum_{t=t}^{t=t+H} inv1t + inv2t &...
3
votes
2
answers
315
views
How do I solve a probability based knapsack problem?
I am looking to maximize my probability of reaching a given target value, by creating multiple groups of 6 items with different means and variances that stay within a weight limit.
This is an example ...
- 31
5
votes
2
answers
344
views
Minimizing under argmin constraint
I have a problem in the form
$$\begin{aligned}
\min_a f(a,b)\\
\text{s.t.}\ b =\ & \arg\min_c g(a,c)\\
& \text{s.t.}\ H(a,c) \leq \vec{0}
\end{aligned}$$
where $f, g, H$ are all ...
- 51
4
votes
2
answers
415
views
Transform nonlinear cost function to get LP or MILP
I'm trying to schedule power of multiple prosumers in a microgrid.
The problem includes a cost function with min and max ...
- 143
-4
votes
1
answer
111
views
Octeract website is not working [closed]
I was recommended to use Octeract. I went to their website but it did not open for me.
https://octeract.com/
Am I the only one facing this problem? Where can I get the student license?
- 3