Unanswered Questions
46 questions with no upvoted or accepted answers
11
votes
0
answers
164
views
Characterizing the solution of a (non) linear maximization program
I have the following maximization program
\begin{align}
\max\limits_{\{q_i\}}&\quad\sum\limits_{i=1}^nq_i \\
\text{s.t.}&\quad\begin{cases} k_j \geq \sum\limits_{i=1}^n q_i^{1 \over \...
- 591
6
votes
0
answers
127
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 ...
- 5,874
5
votes
0
answers
553
views
How to write this objective in CVXPY for quasiconvex programming?
I have the following objective that I want to maximize:
\begin{equation}
\max_{U_T\in \mathbb{R}, x\in\mathbb{R}^T} J_\alpha(U_T) = \frac{\alpha}{\alpha-1}\log\left(\frac{\cosh(U_T)}{\cosh(\alpha U_T)^...
- 86
5
votes
0
answers
135
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 ...
- 2,123
5
votes
0
answers
44
views
In a binary logistic regression context, how to introduce a constraint to model the dependency between consecutive samples
Imagine we are running a logistic regression to identify opportunities for car sale promotion, using previous promotion campaign's result. Each $y$ is the increase of car sale after the promotion.
...
- 5,442
4
votes
0
answers
107
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. $a, b, c$ ...
- 5,442
4
votes
0
answers
36
views
Does knowing the "correct multipliers" for globally optimal first-order critical points help you algorithmically?
Consider the following nonlinear optimization problem:
\begin{align*}
&\min f(x) \\
\text{such that } &h_1(x) = 0, \\
&h_2(x) = 0, \\
& \vdots \\
& h_m(x) = 0,
\end{align*}
where $...
- 1,895
4
votes
0
answers
288
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 ...
- 349
4
votes
0
answers
73
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 ...
- 2,986
4
votes
0
answers
92
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., ...
- 4,010
4
votes
0
answers
251
views
How can I formulate this multi-objective optimization problem?
Now, for each system $X$ $(X=A,B,C,E)$, my objective is
$$\max\min\frac{s_{x_u}}{d_{x_u}}$$
here, $x=a$ for system A, $x=b$ for system B and follows...
and for the whole system, my objective is
$$\max\...
CommunityBot
- 1
3
votes
0
answers
86
views
Looking for an efficient way to solve a fractional problem (affine function over euclidean norm )
While working on optimization issues I encountered the following problem:
$$\left\{\begin{array}{ll}
{\displaystyle \sup_{z\in\mathbb{R}^{m}}} &\frac{ \langle c,z \rangle + \rho}{ \left\|B z\...
- 151
3
votes
0
answers
153
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:
$$\min \sum \limits _i \sum \limits _j (a[...
- 5,442
3
votes
0
answers
135
views
How to find robust counterpart of sum of logit functions?
Suppose function $\mu_i(y):\mathbb{R} \rightarrow \mathbb{R}$ is a logit function, $\mu_i(y)=1/(1+\exp(-y))$. Also, we assume that $\mathbf{x}_i\in \mathbb{R}^d$ and $\theta \in \mathbb{R}^d$. I am ...
- 1,895
3
votes
0
answers
77
views
Linear program with an additional second-degree utility term
I would like to solve a problem obtained from a LP by adding a second degree term to its utility.
A simple example would be the following (with $c_i > 0$):
$$ \min xy - c_1 z_1 - c_2 z_2
\\ \...
- 31
3
votes
0
answers
235
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 ...
- 1,249
3
votes
0
answers
73
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{...
- 543
3
votes
0
answers
62
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(...
- 2,252
2
votes
0
answers
63
views
Special Case of Minimum Cost Flow Problem with Variable Cost
I am working on an optimization problem similar to MCF with variable cost, but with an adjustment in the objective function. The cost function $f$ to minimize that is continuous, piece-wise linear and ...
- 59
2
votes
0
answers
98
views
log-log regression as reward function in optimization problem
Consider the model $\hat{y}_t = e^{\text{trend} + \text{seasonality}} \prod_k^K x_{k, t}^{b_k}$
where $K$ denotes different investment alternatives. You can think that trend and seasonality are ...
- 21
2
votes
0
answers
92
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 ...
- 517
2
votes
0
answers
65
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....
- 5,874
2
votes
0
answers
318
views
Solving minimax problems with Gurobi
I want to solve a problem of the form $\min_x\max_y f(x,y)$ using Gurobi, where $x,y\in [0,1]$.
Is there a simple way to model this in Gurobi? I've seen examples where the domain of $y$ is finite, but ...
- 5,442
2
votes
0
answers
100
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 ...
- 5,442
2
votes
0
answers
308
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 ...
- 1,895
1
vote
0
answers
87
views
volume-weighted mean equality constraints
I have the following optimization objective function for a dynamic pricing problem:
\begin{align*}
sum\_profit = \sum_{i \in sales\_point} \Bigg( constant[i] + {elasticity[i]} \cdot (movement[i] + ...
- 133
1
vote
0
answers
101
views
Converting a Linear Program with TU Constraint Matrix to a Nonlinear Convex Model: Solver Performance?
I'm currently working on a large Mixed Integer Program (MIP) where the constraint matrix is Totally Unimodular (TU), allowing me to model it as a Linear Program (LP) for efficiency, as total ...
- 33.1k
1
vote
0
answers
94
views
Numerical infeasibility for moving numbers along some specific conversion edges to get maximal number on target node from some starter node
I have a problem that can be represented as an optimization problem.
Sometimes, solver engines report infeasible depending on the parameters I have at hand.
The root cause is numeric ranges.
...
- 111
1
vote
1
answer
124
views
Maximizing sum of probabilities with variable distributions
Suppose $\\{X_i\\}$ are binary decision variables and $\\{A_j\\}$ are Skellam random variables with $(\mu_1, \mu_2) = (\sum_i b_{i} X_i, c_j)$. Here, $b_i, c_j \in \mathbb{R}^{\geq 0}$ are constants. ...
CommunityBot
- 1
1
vote
0
answers
28
views
Steepest ascent vector at a point of a constrained nonlinear problem
I'm looking at this article:
"Packing unequal circles into a strip of minimal length with a jump algorithm" (Stoyan et Yaskov, 2014) DOI
In section 5, a nonlinear constrained model is ...
- 2,623
1
vote
1
answer
829
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 ...
CommunityBot
- 1
1
vote
0
answers
59
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
0
answers
68
views
Dual of a quadratic constraint
This is my model.
\begin{align}
\min_x&\quad\sum_{e\in E} X_e p_e \\
\text{s.t.}&\quad\sum_{e \in E: T(e)=i} X_e - \sum_{e \in E: H(e)=i} X_e = \begin{cases}1, \;\text{if}\;i=s\\-1,\;\text{if}...
- 5,442
1
vote
0
answers
651
views
In DOcplex, how can I get value of variable for objective function before solved?
In terms of python based atypical math model as shown below, which is unlike nonlinear or quadratic form in my opinion, I have difficulty in accessing value of variable before optimization as ...
1
vote
0
answers
276
views
Solver issue? Xpress (slp) - Nonlinear - Python - Pyomo
I tried solving my model with xpress:
pip install xpress
And then in the model:
...
- 111
1
vote
0
answers
659
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 ...
- 1,278
1
vote
0
answers
88
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 ...
- 275
0
votes
0
answers
25
views
On Linear Relaxation of Convex Quadratic Maximization over Linear Constraints
Consider the following QP problem, where the matrix $Q$ is positive definite:
\begin{align*}
\max_{x} \quad & x^\top Qx + c^\top x \\
\text{s.t.} \quad & Ax \geq b, \\
& ...
0
votes
0
answers
51
views
Modeling Approach to Adjust linear Elasticity Effect in Pricing Optimization
I am working on a pricing optimization model for a product where the price depends on the competition as well as our costs. The current formulation of the model is:
...
- 133
0
votes
0
answers
51
views
Solving convex separable programming problem using interior point method?
In my engineering application, all decision variables are non-negative and everything is convex separable. In addition to that, the only function that I am trying to approximate with grid point are $f(...
- 1,895
0
votes
0
answers
44
views
Using Knitro or Xpress SLP via FICO Xpress Python API for Local and Global Solve Methods
Can someone guide me on how to utilize the FICO Xpress Python API to invoke Knitro or Xpress SLP, specifically for choosing between local and global optimization methods? I am referring to the version ...
- 23
0
votes
0
answers
58
views
Better formulation of bilinear terms
I am working on an optimization problem where I need to formulate a constraint that represents the total sales value under specific conditions. The challenge lies in creating an expression that ...
- 23
0
votes
0
answers
70
views
Multilinear programming over the simplex
Let $\triangle_3 \in \mathbb{R}^3$ be the $3$-simplex. I am solving a series of multilinear programming problems that looks like this:
$$\text{Maximize}\sum_{0\leq i, j, k \leq 3} A_{i,j,k} x_i x_j ...
- 151
0
votes
0
answers
19
views
Problem in understanding an equation from a paper about iterative Linear-Quadratic Regulator
I'm reading a paper about iterative Linear-Quadratic Regulator (iLQR) and there are a lot of points that I don't understand.
https://homes.cs.washington.edu/~todorov/papers/TassaICRA14.pdf
I think ...
- 5,874
0
votes
0
answers
62
views
How do I solve this non-linear optimisation problem based on simulations?
I have an optimisation problem that is essentially a knapsack problem with a non-linear objective.
I have an input dataframe that contains a row for each item, each item has columns defining its mean ...
- 31
0
votes
0
answers
72
views
Resource selection problem with non-linear objective function
I have an optimisation problem to solve but I can't model it correctly. Any insight is welcome :)
It has been a few years since my optimisation classes in university, and while I have forgotten a lot ...
- 1