Questions tagged [nonlinear-programming]

For questions about mathematical optimization problems involving a nonlinear objective function and/or nonlinear constraints.

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3 votes
0 answers
63 views

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\...
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 views

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 ...
2 votes
1 answer
91 views

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 ...
6 votes
3 answers
430 views

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, \...
2 votes
1 answer
162 views

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 ...
1 vote
1 answer
122 views

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 ...
5 votes
1 answer
251 views

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 views

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 views

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 views

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 views

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 ...
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: ...
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 ...
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 ...
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 ...
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 \...
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 $...
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, ...
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\...
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(...
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 ...
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3 votes
1 answer
382 views

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 ...
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 ...
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 ...
-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?