Questions tagged [nonlinear-programming]

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

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9
votes
2answers
172 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
54 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
180 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
81 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
68 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
51 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
133 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
79 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
166 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
132 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
66 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
177 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
85 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
92 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
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
votes
2answers
135 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
62 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
80 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
56 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
92 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
134 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
131 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
113 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
641 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
83 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
114 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
93 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
105 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
45 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
157 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
81 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
150 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
125 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
votes
0answers
73 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
votes
2answers
253 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
votes
1answer
201 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
votes
2answers
326 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
votes
1answer
192 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
votes
0answers
65 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
votes
2answers
147 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
votes
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
votes
1answer
105 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
votes
1answer
96 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
votes
0answers
49 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
votes
2answers
160 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
votes
0answers
140 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
vote
1answer
95 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
154 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 \\ ...