independentvariable
  • Member for 3 years, 10 months
  • Last seen this week
  • Netherlands
How to optimize three numbers such that their sum is always equal?
2 votes

Formulate $\min \ |a-x| + |b-y | + |c-z|$ $s.t. \ x+y+z = 3d$ Replace $x = 3d - y - z$, you have $\min |a-3d + y+ z| + |b-y| + |c-z|$. Linearize it by replacing: $\min t_1 + t_2 + t_3 \\ s.t. \ -...

View answer
Is there a theory for heuristics in the field of optimization?
Accepted answer
2 votes

There are great theories behind most of the metaheuristics. Otherwise, it is not reliable to use them. One example is Simulated Annealing. It is approaching the true optimum if you increase the ...

View answer
Determine the optimal point satisfying the given condition
Accepted answer
1 votes

The optimal solution is at $x = [1.7,1.9]^T$, so your answer is correct. Also, the second coordinate (I believe this is $x_2$) is greater than the first one. Maybe "they shall differ at least 1" ...

View answer
A system of linear inequality is equivalent to a system of strict linear inequality
1 votes

Firstly, please notice that the link you shared is not saying a point $x_i$ satisfying the first set satisfies the second. Instead, it says that if you write such a classification in the $1^{st}$ set, ...

View answer
infimal convolution on conjugate of the sum of convex functions
Accepted answer
0 votes

Ok, I solved. here they show that $(\sum\lambda_j g_j)^* =(\lambda_1g_1)^* \Delta (\lambda_2g_2)^*\Delta \ldots $ where $\Delta$ is the infimal convolution operator. Next, apply the definition of inf ...

View answer
Substitution in Normal Distribution integral calculation
0 votes

I just found a very helpful Wikipedia article, easy to understand: https://en.wikipedia.org/wiki/Integration_by_substitution#Application_in_probability

View answer
Simple but not simple Nonconvex Optimization Problem
Accepted answer
0 votes

First of all, it is hard to understand your main question. 'Simple but not simple' is not reflecting your wish to solve a nonconvex problem. I assume your variables are continuous, e.g. $\tau \in \...

View answer
How to calculate an optimal combination of metals based on price
0 votes

Let $x_i,$ denote the type of alloy for all $i=1,2,\ldots,8$. For example, $x_1=iron, x_2=carbon $ etc. $UB_i$ denotes the upper bound possible for production of material $i$ (in percentage), $LB_i$ ...

View answer
Karush-Kuhn Tucker (KKT) optimality conditions for the following problem.
0 votes

Note that this is not a convex optimization model (check the hessian of the objective function). So in order to find the optimal point you may check all the KKT solutions. I am not writing them one by ...

View answer
A system of linear inequality is equivalent to a system of strict linear inequality
0 votes

They are not equivalent. There is no assumption about $b$. So $⟨a,x_i⟩+b$ can be i.e. $0.5$ when $y_i = 1$ and not fulfill the second condition. I think you should give more details about $a$ and $b$ ...

View answer
How to prove that lattice width is attained?
Accepted answer
0 votes

The answer is mostly in Proposition 2.3. of: Draisma, J., McAllister, T. B., & Nill, B. (2012). Lattice-Width Directions and Minkowski's 3rd-Theorem. SIAM Journal on Discrete Mathematics, 26(3), ...

View answer
LP relaxation of the symmetric TSP problem integrality for n=5
Accepted answer
0 votes

Solved it. Grötschel and Padberg (1979) proved that $0 \leq x \leq 1$ defines facets of the TSP polytope when n=5. This fact and redundant subtour elimination constraint gives the perfect formulation....

View answer