Questions tagged [nonlinear-programming]
For questions about mathematical optimization problems involving a nonlinear objective function and/or nonlinear constraints.
82
questions
0
votes
0answers
14 views
Does not Pyscipopt handle nonlinear objective function?
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 ...
4
votes
1answer
58 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
72 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
547 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
74 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
98 views
Free solver for MINP problems
I have a mixed-integer nonlinear programming (MINP) problem.
Is there a free solver for such a problem?
5
votes
1answer
88 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
0answers
54 views
How can I make the constraint based on logarithm and absolute value linear?
I have two constraints of the form
$$\log\left(1+|b_k|^2+\sum_{j=1,j\neq k}^{K}|b_j|^2\right)\ge \log(2)x_k+y_k\quad\forall k, k=1,\cdots,K$$
and
$$1+\sum_{j=1,j\neq k}^{K}|b_j|^2 \le e^{y_k^{(0)}}(...
4
votes
0answers
60 views
“Rank 1” type constraint $X=vw^\top$: MILP representation? Convex relaxation? Other tractable approach?
Suppose $X\in\mathbb{R}^{m\times n}$, $v\in\mathbb{R}^m$, $w\in\mathbb{R}^n$ are variables from an optimization problem, which also includes the constraints:
$$0\le v\le a$$
$$0\le w\le 1$$
$$w_1+\...
2
votes
0answers
36 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
99 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
77 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 ...
8
votes
1answer
140 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
101 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
67 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
119 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
174 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
305 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 ...
5
votes
1answer
182 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
$$\begin{align*}
&\min f(x)\\
&x \in X\\
&g(x) \le 0
\end{...
2
votes
0answers
59 views
Optimizing with a logistic function
I have a system in which I want to maximize the value of some function $f(x_T, y_T)$.
The time evolution of the system is described by some functions:
$$
\begin{align}
\frac{dx}{dt}&=\alpha \frac{...
4
votes
2answers
134 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
99 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
89 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
47 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
154 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
124 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
77 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
votes
1answer
96 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
votes
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
votes
0answers
50 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
votes
3answers
997 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 ...
3
votes
1answer
117 views
Rolling Horizon Methods in Knitro
I am trying to solve an NLP using the Knitro solver, but I am beginning to think that I will not be able to solve the model because it is too complex. I have heard that "rolling horizons" can be used ...
5
votes
2answers
122 views
Minimizing $x_1/x_2$ over a simplex in the positive orthant
I need to solve the following problem
\begin{align}\min&\quad x_1/x_2\\\text{s.t.}&\quad Ax \leq b\\&\quad x > 0\end{align} where $A$ is a positive matrix.
The best thing I can think ...
4
votes
1answer
112 views
Software for multi-objective optimization
I am looking to solve a multi-objective chance-constrained blending problem. Are there any suggestions about the software to use to try and solve a problem like this?
4
votes
1answer
84 views
How to convert non-normal probabilistic constraints to deterministic ones for mathematical modelling?
I am working on a chance-constrained optimisation model that takes into account uncertainty. I am aware of how to convert constraints that are of a probabilistic nature into the equivalent ...
6
votes
1answer
75 views
Nonsmooth constrained convex optimisation: convergence results?
I am working on a projection problem on a very large set of highly related constraints:
\begin{align}
\min_x & \quad\|x-x_k\|_2^2 \\
\mathrm{s.t.} & \quad\max_{T\in\mathcal{T}} \sum_i \frac{...
13
votes
1answer
87 views
Benders subproblem feasible region dependent upon solution master problem
Suppose I want to solve a naturally MINLP problem of the following form:
$$
\min_{x,y} \{c'x + y \mid Ax \leq b, Dx + Ey \leq f, G(x)y\leq g, x \in \mathbb{Z}, y \in \mathbb{R}^+\}
$$
Here $G(x)$ ...
8
votes
1answer
175 views
Can Gurobi or CPLEX handle nonlinearly constrained problems?
Though my title is quite general (please feel free to edit), indeed, I wonder if the following models can be solved in Gurobi or CPLEX. Model 2 is just an alternative one to Model 1. Although we ...
4
votes
1answer
77 views
Dealing with a non-convex problem
I have the following objective function. The variables: $h_p$, $e_{trs}\left(h_p\right), w_{trs}\left(h_p\right)$ are all non-negative continuous. $T,R,S,\pi_{trs}$ are polynomially-sized sets. All ...
6
votes
4answers
149 views
Sequential quadratic programming source
What are the good text books to learn SQP? Are there any online courses that you can suggest?
6
votes
1answer
87 views
How to minimize a weighted sum of RMSE-like terms?
I am trying to solve the following problem: \begin{align}
\min&\quad f(x) = \sum_{i=1}^{n}{a_ix_i} + \sum_{i=1}^{n}{b_i\sqrt{\sum_{j=1}^{m}{\left(y_{i,j}-x_i\right)^2}}}\\\text{s.t.}&\quad
x_{...
8
votes
2answers
298 views
How can I transform this MILP into an LP problem?
I have a MILP problem with one of the constraints is given below. Sometimes, even for a small-sized problem, the solver takes a very long time to find a solution. What could be an efficient ...
12
votes
1answer
259 views
Linearization of the product of two real valued variables - Binary expansion approach
I want to minimize the following objective function:
\begin{align}\min &\quad x\cdot y\\\text{s.t.}&\quad2 \le x \le 5\\&\quad5 \le y \le 10.\end{align}
Since the objective function is ...
12
votes
2answers
212 views
Can Tuning Knitro Solver Considerably Make A Difference?
I have an NLP that I am hoping to solve with Knitro and I am aware of a multitude of different settings that you can "tune" in order to improve solution performance. I am not familiar with ...
12
votes
1answer
362 views
Suggested Resources for Non-Linear Optimization
I recently completed an undergraduate course in Linear Programming and Operations Research. I am willing to look into advanced concepts and Non-Linear Optimization algorithms and also, their method of ...
8
votes
1answer
160 views
Is this formulation linear or non-linear?
Can you help me figure out if this formulation constitutes a non-linear problem? I believe It is a linear problem but my solver (GAMS) is unable to produce a acceptable solution.
$x,y$ and $\text{...
7
votes
2answers
439 views
Why does a Max constraint work, but this non-negativity constraint does not?
Suppose I have the following constraint: \begin{align}x_{t} &= x_{t-1} + y_{t-1} - z_{t-1}\\x_{t} &\ge 0\end{align}
From my limited experience in coding my own problem, I have found that my ...
9
votes
1answer
153 views
Solving convex programs defined by separation oracles?
General question: What software can solve convex programs defined by a separation oracle?
The objective function is concave, and the feasible set is a polytope. By a separation oracle I mean that I ...
