Questions tagged [nonlinear-programming]

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

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0answers
37 views

Lagrangian dual function of KKT

I encountered a nonlinear problem with a non-convex objective function and an equality constraint, so to decide whether there exist a global optimal, I was told to compute the Lagrangian dual function....
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0answers
51 views

How to calculate the time complexity of a Heuristic Algorithm?

I have a binary integer programming problem. I solve it with a heuristic approach. How can I calculate the time complexity of the heuristic algorithm?
5
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0answers
112 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
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1answer
132 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
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1answer
72 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-...
1
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1answer
158 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
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1answer
124 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
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0answers
61 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
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1answer
152 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
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1answer
79 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 ...
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1answer
89 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
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3answers
1k 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
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2answers
131 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
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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
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0answers
56 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 ...
2
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1answer
73 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
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1answer
50 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
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2answers
89 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
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0answers
117 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
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1answer
92 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
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2answers
98 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
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1answer
610 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
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1answer
79 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
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1answer
110 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
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1answer
92 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
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1answer
102 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
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0answers
42 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
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1answer
137 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
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1answer
79 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
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1answer
149 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
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2answers
112 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 ...
5
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0answers
69 views

Is there a way to use lazy constraints with Baron?

I am solving a non-linear mixed-integer programme with BARON. The objective function looks like $\big( \sum_i x_i \big) \cdot \big(\prod_i e^{-y_i}\big)$ (binary $x$ and real-valued $y$) and it has ...
2
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2answers
189 views

Pyomo + Ipopt. Speed Issue

I am using Pyomo + Ipopt as solver to solve a NLP problem. The problem is not extremely complex in terms of dimensionality and ...
6
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1answer
193 views

Linearizing a program with multinomial logit in the objective

I have a nonlinear problem as follows: \begin{align}\min&\quad\sum_{k=1}^{K}\left|y_k - \sum_{i=1}^{N} \frac{e^{x_{k}^{i}}}{\sum_{j=1}^{K} e^{x^{i}_{j}}}\right|\\\text{s.t.}&\quad x^i_{j} \ge ...
5
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2answers
319 views

Failing to meet a constraint in a NLP problem

I have a NLP problem at hand, which I am trying to solve via Pyomo + ipopt. I try to run several different instances of the optimizer with different conditions, out ...
4
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1answer
190 views

Trouble understanding a passage in Nonlinear Programming by Bertsekas

I am reading Nonlinear Programming by Bertsekas, and the chapter on duality starts like this: we define the primal problem as $$\begin{align*} &\min f(x)\\ &x \in X\\ &g(x) \le 0 \end{...
3
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0answers
64 views

Optimizing with a logistic function

I have a system in which I want to maximize the value of some function $f(x_T, y_T)$. The time evolution of the system is described by some functions: $$ \begin{align} \frac{dx}{dt}&=\alpha \frac{...
4
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2answers
146 views

Constraint $x'Ax = 0$, where $x$ and $A$ are both optimization variables

I'm trying to solve the following optimization problem: $$ \min_{x, \phi} x \quad \text{s.t.} \quad \sum_{s,t = 1}^n \left(m_{s,t} x -v_{s,t} \right)\phi_s \phi_t = 0 , \quad \lVert \phi \rVert = 1$$ ...
10
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6answers
2k views

Nonlinear integer (0/1) programming solver

I have the following optimisation problem.\begin{align}\max&\quad\sum_i\sum_j\sum_k x_{ji}y_{kj} \operatorname{cost}(i,k)\\\text{s.t.}&\quad\sum_j x_{ji}=1\quad\forall i\\&\quad\sum_k y_{...
7
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1answer
104 views

Minimizing sum of functions with pairwise dependence

I have formulated a problem where I need to minimize the sum of $N$ functions, with only pairwise dependence between the functions (any single constraint involves only two functions having adjacent ...
6
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1answer
94 views

Does strong duality hold when I dualize only a subset of the constraints?

Suppose I know that for some non-convex program: \begin{align}\min_x&\quad f(x)\\\text{s.t.}&\quad g_i(x)\leq 0, i \in C\end{align} strong duality holds for this problem. Now, suppose I form ...
3
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0answers
48 views

Linearisation using SOS2

I am trying to linearise the following expresssion. $C(k) = B(k) e^{-d(k)}, B(k) \ge 0 , d(k) \ge 0 $ I am trying to do this by using SOS2 sets. I set $X(k) = e^{-d(k)}$ and I get $C(k) = B(k) X(...
7
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2answers
159 views

Find Euclidean sub-distances for a given distance matrix

Assume I have a matrix $(d_{ji})_{ij}$ of distances between points $i$ and $j$. These distances could be anything fulfilling the triangle inequality. Now I would like to find coordinates $(x_i,y_i)$ ...
2
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0answers
132 views

Gurobi is unable to give an optimal solution even when it exists

I am trying to solve Logarithmic Fuzzy Preference Programming (LFPP) for criteria weight evaluation, based on fuzzy comparisons between criteria, and I am solving it with Gurobi in Python 2.7. It is a ...
1
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1answer
86 views

Simple nonlinear programming using convexity analysis and KKT

I want to solve the following two-variate nonlinear programming using KKT conditions: $$ \begin{align} \begin{split} \max \quad & 15 \sqrt{x_{1}} + 16 \sqrt{x_{2}} \\ \text{s.t.} \quad &...
1
vote
1answer
150 views

How do I solve this Optimization problem?

Optimization of a simple expansion problem minimise: $$ \sum_{t=1}^{5}\left[\sum_{i=1}^{2}x_{i,t}CC_i\left(\frac{1+EIC}{1+r}\right)^t+UE_t*C_{UE}\right] $$ subject to: $$ 0 \leq x_{i,t} \leq 5 \\ ...
2
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1answer
106 views

How to detect unbounded problems

How can I algorithmically detect whether an (MI)NLP problem is unbounded or not? Finding a source for this has proven tricky, because people in the literature seem to talk a lot about what to do if ...
4
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2answers
153 views

Is There Another Way To Code The Idea of a MAX Constraint Without The Use of Binary Variables?

I have a constraint of the following form that describes the growth of trees, where the population of trees in period $t$ is the previous period's population minus some trees infected with a virus: $...
4
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0answers
55 views

Identifying saddle point in constrained optimization

Suppose we are minimizing $f(x)$. The first order necessary condition of $x^*$ being local minmum is: $$\nabla f(x^*)= \mathbf{0}.$$ For sufficiency, we check if also $\nabla^2f(x^*) \succ 0$, i.e., ...
6
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3answers
1k views

Is it abnormal for a model to take 8+ hours to solve?

I am building my first optimization model, it is quite large and also a non-linear problem. I have had my model solving on the NEOS Optimization Server and after 8 hours of trying to solve, the server ...