Questions tagged [nonlinear-programming]

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

9 questions with no upvoted or accepted answers
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11
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129 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 \...
6
votes
0answers
74 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 $\...
5
votes
0answers
65 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 ...
5
votes
0answers
31 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. ...
4
votes
0answers
47 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
votes
0answers
188 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\...
3
votes
0answers
46 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
votes
0answers
58 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{...
2
votes
0answers
91 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 ...