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Results tagged with nonlinear-optimization
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user 141766
Nonlinear objectives, nonlinear constraints, non-convex objective, non-convex feasible region.
0
votes
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Round Robin volleyball Tournament
Assuming binary decision variable $x_{ijd}$ indicates whether teams $i$ and $j$ play each other on day $d$, introduce a decision variable $z$, and maximize $z$ subject to linear constraints
$$z \le \f …
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1
vote
Optimal covering of line subsegments using a given set of disks
You can formulate this as a set covering problem. For each circle $j$, define a binary variable $x_j$ that indicates whether circle $j$ is selected. Let $C_i$ be the set of circles that intersect li …
- 5,029
1
vote
Transformation of an unconstrained binary quadratic optimization problem into a constrained ...
Yes, the linearization of a product of binary variables is well known:
https://or.stackexchange.com/questions/37/how-to-linearize-the-product-of-two-binary-variables
- 5,029
0
votes
Accepted
How to find the maximum of a sum of squares of sums?
You can solve the problem via binary quadratic programming as follows. Let binary decision variable $x_{id}$ indicate whether row $i$ is rotated $d$ places. The problem is to maximize
$$\sum_{j=0}^{ …
- 5,029
3
votes
How quickly can this IQP or its MILP relaxation be solved
For binary $P$, we have $\min\{P_{k,i},P_{l,j}\} = P_{k,i} P_{l,j}$. In your linearization, you have introduced $r_{i,k,l,j}$ to represent this product. Because of the linear constraints $$\sum_k P_ …
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2
votes
Accepted
How to integrate an indicator function/constraint into the cost function of a linear program?
I will simplify the notation to illustrate the idea. You want to minimize $$\sigma \max\left(\sum_{i,j} d_{ij} x_i x_j - \alpha, 0\right).$$
Introduce binary decision variable $y_{ij}$ to represent t …
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1
vote
How to solve the optimization problem $\max_{\mathbf{w}}\sum_i\text{sign}(\mathbf{w}^T \math...
Let $L_i$ be a constant lower bound on $\mathbf{w}^T \mathbf{x}_i$.
You can linearize the problem by introducing binary decision variable $y_i\in\{0,1\}$ to indicate whether $\mathbf{w}^T \mathbf{x}_i …
- 5,029
1
vote
What is the computational complexity of the calculation of $ \Psi(x) $?
This is a variant of the integer equality knapsack problem and can be solved via dynamic programming. The complexity is described here.
For a DP recursion, first define
$$\Psi_k(x):=\min_{\begin{arra …
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2
votes
Optimization over permutation
By introducing a dummy depot node, you can think of this as a special case of the time-dependent traveling salesman problem. The dummy node is adjacent to all other nodes, with zero-cost links.
You mi …
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