Unanswered Questions
61 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
6
votes
0
answers
145
views
Cases where RLT/SDP relaxation does not work well with standard quadratic optimization
(For people who don't know what RLT is): I am maximizing an indefinite quadratic function over a standard simplex, i.e., the standard quadratic optimization problem. A well-known approach is to relax ...
- 4,010
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
193
views
Fast solvers for LASSO-type non-convex optimization problems
Given $y \in \mathbb{R}^{n \times 1}, X \in \mathbb{R}^{n \times p}$, $p > n$, assume a LASSO-type optimization problem in the form of
$$ \hat\beta=\underset{\beta}{\operatorname{argmin}}\frac{1}{2}...
- 141
4
votes
0
answers
92
views
Identifying saddle point in constrained optimization
Suppose we are minimizing $f(x)$. The first order necessary condition of $x^*$ being local minmum is:
$$\nabla f(x^*)= \mathbf{0}.$$
For sufficiency, we check if also $\nabla^2f(x^*) \succ 0$, i.e., ...
- 4,010
4
votes
0
answers
160
views
Strong Duality and Slater Condition
I am studying the Duality Chapter of Convex Optimization by Boyd. Is it possible that strong duality holds for non-convex optimization? If yes, is there any specific condition? And, what is the ...
- 2,160
4
votes
0
answers
251
views
How can I formulate this multi-objective optimization problem?
Now, for each system $X$ $(X=A,B,C,E)$, my objective is
$$\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
55
views
Are there algorithms for minimizing a sum of convex and non-convex/non-concave functions?
Consider the problem
\begin{equation}
\begin{aligned}
\min_{x}
\quad & f(x) + g(x), \\
\textrm{s.t.} \quad & x \in X
\end{aligned} \tag{1}
\end{equation}
where $X \subset \...
- 639