Questions tagged [nonlinear-programming]
For questions about mathematical optimization problems involving a nonlinear objective function and/or nonlinear constraints.
118
questions
3
votes
0answers
64 views
Linear program with an additional second-degree utility term
I would like to solve a problem obtained from a LP by adding a second degree term to its utility.
A simple example would be the following (with $c_i > 0$):
$$ \min xy - c_1 z_1 - c_2 z_2
\\ \...
2
votes
1answer
132 views
Linearizing division of two variables
For all $i \in I,j\in J$ and $k\in K$, define variables $x_{ij}, z_{ijk}\in\{0,1\}$, $y_{ij}\geq 0$ and constants $c_j, e_{ijk}, d_j, f_j >0$.
We have the following constraint
$$\sum_{j\in J_1}c_j\...
4
votes
1answer
200 views
Can we simplify (perhaps linearize) this constraint?
We are dealing with a stochastic model and one of the constraints is
\begin{align}
y_j=\frac{\sum_{i \in I}\sum_{k \in K}\mathbb{E}\left[X_{ik}^2\right]x^k_{ij}}{\sum_{i \in I} \sum_{k \in K} \mathbb{...
0
votes
0answers
45 views
Controlling IPOPT options with pyomo doesn't work
I am using IPOPT solver for solving KKTs conditions (a bunch of equality constraints and complementarity conditions).
For assigning the solver for complementarity problem, I use the command line below:...
4
votes
0answers
212 views
Linearize a highly non-linear objective function
[EDIT] : The formula below is updated to remove the radical, 0.5 in the term $(I_{i,v} \cdot \Delta t)$ and constant temperature $T$ replces temperature as function of current.
[EDIT] :The values of ...
-3
votes
2answers
127 views
No value for uninitialized NumericValue object
I'm working on an optimization model in python with the pyomo library. However I'm getting an error message in python that I cannot seem to understand. The code and error message is below.
My code is
<...
4
votes
1answer
123 views
Python library to solve nonlinear problems
What is the best python library to solve nonlinear problems? PuLP can solve only linear problems like $\max15000Z_7 + 350D_{73}Z_7 - 15000Z_8 + 350D_{86}Z_8$.
6
votes
1answer
440 views
Is there any open source quadratic programming solver with C# API
I have a quadratic programming model (i.e., quadratic objective function and linear constraint) and, I want to solve it on an open-source solver. Since our project developed on C#, we also would like ...
3
votes
1answer
63 views
Convex-Constrained Nonconvex-Nonconcave Minimax Problem
In the mathematical optimization theory, I have taken a glance at many papers which deal with the unconstrained convex-concave or nonconvex-concave minimax optimization, i.e.,
$$
\min_{x\in X}\ \max_{...
4
votes
2answers
710 views
Should all decision variables be present in Objective function?
This might be a very basic question for this community. I am reading an article and I think I have some confusion about formulating a problem. My understanding is that all decision variables should ...
2
votes
0answers
47 views
Two-stage stochastic with non-linear recourse
I am working on a two-stage facility location problem as I described in this question.
I am solving it with the L-shaped method (Benders decomposition). The cost value between each $(i,j)$ is a ...
0
votes
2answers
60 views
Branch and bound method for solving non-convex integer non-linear multi-objective optimization problem?
Following are the characteristics of my problem:
Objective function: two non-linear functions and one linear function
Decision variable: two integer variables ($X_1$ and $X_2$)
Constraint: three (two ...
5
votes
1answer
174 views
What methods are used to solve multi-objective optimization problem with non-linear objective functions and integer decision variables?
Case 1: NLP
When either the objective function or at least one of the constraints or both are non-linear it is a NLP. We use generalized reduced gradient or Quadratic Programming to solve NLP. However,...
4
votes
1answer
150 views
How to linearize a non-convex optimization objective function?
The non-convex multi-objective optimization problem in my case is defined below:
Objective 1: Minimize $f_1(X_1,X_2)=C_0+C_1(1/X_1)+C_2(X_2/X_1)+C_3X_1+C_4X_2+C_5(X_2^2/X_1)$
Objective 2: Minimize $...
3
votes
1answer
159 views
pyomo/ipopt: nonlinear network optimization not converging
The question (very short version)
Why can I not decrease the lower boundary for the decision variable model.v_dot (see implementation) below 30 ? As soon as I do so,...
9
votes
2answers
181 views
MINLP involving integrals, sparse matrices and CDF of random variables. Best environment?
INTRODUCTION
My research often involves solving MINLP problems with few constraints (usually two) and not many variables (say between one and three integer ones, and between one and five real-valued ...
4
votes
1answer
67 views
Is it always possible to optimize a multivariate function sequentially?
Suppose we have a multivariate function like $f(x,y,z)$ which should be maximized with the constraints $g_i(x,y,z)\le 0 \quad \forall i$. The general rule is to use KKT conditions and derive all KKT ...
1
vote
3answers
201 views
Prove NP Hardness for non-convex multi-objective optimization
The multi-objective optimization problem in my case is non-linear as it consists of three objective function of which two are nonlinear function and the third is a linear function. Lets say objective ...
1
vote
1answer
84 views
Maximization of a differentiable and nonlinear function over a bounded space
I have a nonlinear bi-variate optimization problem like $\max \: f(x,y)$ where $f(x,y)$ is a nonlinear and differentiable function of both variables, and $0\le x\le 1$, $\:0\le y \le ub$. In order to ...
2
votes
1answer
71 views
Subtracting Values from a Positive semidefinite Matrix in a Semidefinite Program
I'm trying to construct an SDP relaxation for a non-convex quadratic program ($x^{\intercal}\mathbf{H}x$) with the following objective function:
\begin{equation}
x_{11}y_{11} + x_{12}y_{12} + x_{21}y_{...
1
vote
0answers
76 views
Solver issue? Xpress (slp) - Nonlinear - Python - Pyomo
I tried solving my model with xpress:
pip install xpress
And then in the model:
...
6
votes
0answers
120 views
Water quality component optimization
I have an optimization problem that I'm attempting to tackle. As you can see in the image below, there's a graph network through which water flows. I've drawn out the problem in the image to explain ...
6
votes
1answer
136 views
Two equivalent soft constraint implementations
Take the following optimization problem:
\begin{align}\min_x&\quad f(x)\\\text{s.t.}&\quad g(x)\le0\end{align}
with $f$ and $g$ nonlinear functions. Suppose I want to relax the constraint by ...
0
votes
1answer
82 views
How to solve this clustering problem with heuristic or meta-heuristic approach?
I have clustering problem with servers and users. This is different to the one posted in https://math.stackexchange.com/questions/4088441/what-will-be-an-efficient-joint-clustering-solution-to-this-...
2
votes
1answer
173 views
Which linearisation technique is correct?
I have the objective function (Maximally Diverse Grouping Problem) as
$$\max\sum_{g=1}^G\sum_{i=1}^{N-1}\sum_{j=i+1}^{N}d_{ij}x_{ig}x_{jg}$$
Here, $d_{ij}$ are known parameters, and $x_{ig}$ and $x_{...
1
vote
1answer
148 views
Non-linear optimization local or global solution
In an NLP, I have a constraint that I would like to formulate in a convex manner preferably without introducing binary variables and/or big M formulations if possible. The actual problem is non-convex ...
4
votes
0answers
67 views
How can non-polyhedral sets be investigated?
To derive problem-specific cutting planes for some given problem (think something like TSP problem), one common way is to study small examples. To this end, one can create small instances for the ...
4
votes
1answer
249 views
how to implement an optimization function with polynomial in Gurobi (Java)
I have the following problem:
I have an objective function with the optimization variable $x$, which looks simplified like this:
$ZF = (a+b)*(x+1)$
Here $a$ is simply a constant value.
However, behind ...
0
votes
1answer
105 views
How to linearise this nonlinear constraint?
I have a constraint in the form
$\sum_{n=1}^{N}x_{m,n}\omega_{m,n}\ge (t_u-1)\beta_u, \forall u, u=1,2,\cdots, U$
where $x_{m,n}$ is binary variable
$t_u$ and $\beta_u$ are continuous optimization ...
1
vote
1answer
98 views
How can I linearise this nonlinear proportional relation constraint?
My optimisation problem has a constraint in the form
\begin{equation}
\begin{array}{*{35}{l}}
\text{}\hspace{16.5mm}\text{ C4:} \hspace{2mm}\sum_{u=1}^U d_{u,1}L_{u}:\sum_{u=1}^U d_{u,2}L_{u}:\cdots:\...
6
votes
3answers
2k views
Is a mathematical programming problem with no objective function an optimization problem?
I have a "mathematical programming" (MP) problem that does not have an objective function. Namely, I want to find a vector that satisfies all constraints (no optimization involved, right?). ...
4
votes
2answers
139 views
Continuous water-filling optimization problem
Disclaimer: this question has been previously posted on Math StackExchange. I reposted it here since I did not receive any satisfactory answer there and a user suggested to re-post it here.
Let $x\in\...
10
votes
2answers
1k views
Trustful Nonlinear Programming
Is it possible for an NLP solver to claim that a knowingly feasible problem is infeasible?
Shouldn't the solver be able to provide a solution (of course not necessarily the global optimum but a ...
3
votes
0answers
69 views
Solving a nonlinear model with constraints of exponential functions and continuous variable multiplications
I have a nonlinearly-constrained model and wonder if a nonlinear solver like Ipopt or Knitro can solve the problem.
Briefly, my objective function is linear. I have the following variables with their ...
3
votes
1answer
84 views
Smooth approximation of $\max(f_1(x),f_2(x),\cdots,f_n(x))$
In the GAMS documentation concerning non-smooth optimization I found the following statement:
A smooth approximation for $\max(f(x),g(y))$ is as in the following example code:
...
3
votes
1answer
57 views
Maximize $\sum_{i=1}^n 1/x_i$ subject to an SDP constraint
I would like to solve the following problem: \begin{align}\max_{x_1, \ldots, x_n}&\quad\frac{1}{x_1} + \frac{1}{x_2} + \cdots + \frac{1}{x_n}\\\text{s.t.}&\quad\sum_{i=1}^n x_i A_i \succeq A_0\...
3
votes
2answers
94 views
Scheduling Problem With Identical Machines
I am working on a nonlinear scheduling problem that minimizes the electricity cost of a facility. This system includes a number of identical machines that consume power and produce a product. When the ...
1
vote
0answers
160 views
Doesn't Pyscipopt handle nonlinear objective functions?
I am trying to solve a large-scale nonlinear problem. Below is the objective function coded for pyscipopt. I have some loops over a list of tuples (r,p,s) in the list RouteTimeStop, and the only ...
3
votes
1answer
205 views
Ipopt (probably) fails to solve a nonlinear problem, what is next?
I am trying to solve a nonlinear problem with only a set of continuous variables (where the nonlinearity stems from negative inconsistent - across differently indexed variables - large powers), e.g., ...
5
votes
2answers
137 views
Solve nonlinear programming problems practically
In an exam, I studied Theoretical approaches to converting constrained minimum problems into unconstrained minimum problems. Specifically:
KKT conditions
Projection Gradient Descent
Penalty and ...
16
votes
1answer
669 views
Deep Reinforcement Learning for General Purpose Optimization
Recently, I attended a very nice talk given by someone at the place I work about applying Deep Reinforcement Learning (DRL) for a design optimization problem. It was particularly interesting to me ...
3
votes
1answer
90 views
Optimizing black-box finite element model
I'm trying to understand what my options are for optimizing a black-box simulation (output from a commercial, closed source finite element solver).
An example problem is the following. We have a ...
4
votes
1answer
123 views
Free solver for MINP problems
I have a mixed-integer nonlinear programming (MINP) problem.
Is there a free solver for such a problem?
4
votes
1answer
114 views
Contiguous service area constraint
Background: I have a set of ZIP codes (e.g., all of the state of Wisconsin), and am trying to figure out an optimization-based approach to identify a subset of these ZIP codes for a logistics service ...
3
votes
1answer
114 views
"Rank 1" type constraint $X=vw^\top$: MILP representation? Convex relaxation? Other tractable approach?
Suppose $X\in\mathbb{R}^{m\times n}$, $v\in\mathbb{R}^m$, $w\in\mathbb{R}^n$ are variables from an optimization problem, which also includes the constraints:
$$0\le v\le a$$
$$0\le w\le 1$$
$$w_1+\...
1
vote
0answers
47 views
active set method guaranteed convergence
I'm using Active Set Method to solve a nonlinear optimization function minimizing a convex function over a polyhedron of 2 linear inequalities starting at an interior point $x_o$ At this point is it ...
3
votes
1answer
181 views
Using log optimization function in Gurobi
I'm trying to use Gurobi to model an optimization max function whose objective function is $$f(x)=\frac{r^Tx}{x^TQx}.$$
Thus maximizing this function $f(x)$ is the same as maximizing $\log f(x)$ and I ...
3
votes
1answer
85 views
What type of model is this
I was trying to find a name for the following model; is it mathematical programming, constraint programming, convex optimization, but as I can see, none of them has a continuous parameter $t$ like in ...
7
votes
1answer
153 views
Is the solution of a convex combination of the objective in simple problems a convex combination of the solutions of the same problems?
Let $\mathbf{A}=\left(a_{ij}\right)$ be a $n\times J$ matrix with $a_{ij}\geq 0$, $n>J$ and such that no row has all its entries equal to zero, and each column has at most one zero. Let also $\...
4
votes
2answers
146 views
How to deal with an optimization problem that have a sum of nonlinear functions of Z as a constraint when Z is the quantity to be minimized?
I have to minimize a quantity $Z$ subject to the following constraints:
$$ w_1 + w_2 + w_3 = 1 \tag{1}$$
$$ \frac{f_1(w_1 Z) + f_2(w_2 Z) + f_3(w_3 Z)}{Z} \ge k \tag{2}$$
where $k$ is a known ...
