# Tag Info

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### What are the advantages of commercial solvers like Gurobi or Xpress over open source solvers like COIN-OR or CVXPY?

Disclaimer: I am currently working for a commercial solver company (Gurobi) and have worked before on another commercial solver (IBM CPLEX). Hence, my opinion may be biased, but still I am trying to ...

### What are the advantages of commercial solvers like Gurobi or Xpress over open source solvers like COIN-OR or CVXPY?

No, the situation isn´t the same for OR libraries. There are several reasons for this, among them being Performance: The difference is relevant, with an emphasis on Mixed Integer Programming (linear ...
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### What are the advantages of commercial solvers like Gurobi or Xpress over open source solvers like COIN-OR or CVXPY?

I think the short answer is: speed. Most optimization problems solved in the OR world are computationally intractable, they cannot be solved in reasonable time as the size of the data increases. A ...
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### Constrained optimization of a sum

You also need to account for Lagrange multipliers for the bound constraints $-1\le x_i \le 1$. Given all $a_i>0$, the (linear programming) problem is to maximize $\sum_i a_i x_i$ subject to \begin{...
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### What are the advantages of commercial solvers like Gurobi or Xpress over open source solvers like COIN-OR or CVXPY?

(Full disclosure: I run a solver company) The state of the art Unlike ML, in the optimisation space commercial software is unfortunately on average superior to open-source alternatives. This does not ...
• 11.9k
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### How do we formulate a problem where the decision variable has an index that is also a decision variable?

Let binary decision variable $y_{ij}$ indicate whether $x_i = a_j$, and impose linear constraints \begin{align} \sum_j y_{ij} &= 1 &&\text{for all $i$} \tag1\label1 \\ -(1 - y_{ij}) \le ...
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### Genetic Algorithm

Not exactly what you are needing, but DEAP allows to pass constraints as a decorator: https://deap.readthedocs.io/en/master/tutorials/advanced/constraints.html .
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### Genetic Algorithm

PyGAD seems to be a decent library, although I have never tested it myself. The documentation looks very complete, with good examples.
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### Augmented Lagrangian Function for Semidefinite Programming Problems

My way of reading it is $\langle X, \mathcal{A}^*(y)+S-C\rangle = \langle X, \mathcal{A}^*(y)-C\rangle + \langle X,S \rangle$. The first term is your standard inner product between dual variable and ...
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### MINLP involving integrals, sparse matrices and CDF of random variables. Best environment?

I suggest you have a look at LocalSolver to solve your problem. It is free for basic research and teaching. Contrarily to its name suggests, LocalSolver is a global optimization solver. It handles ...
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### Is there a name for this type of integer programming?

You have is a linear integer programming problem with a generalized objective function of the form: $$g(x) = f\big( \sum_i C_i x_i \big).$$ If $f(X) = {\rm tr}(X)$, then $g(x)$ is an ordinary linear ...

### Convex optimization with linear constraints. Can I solve it analytically?

You are going to be dealing with various cases depending on the values of $c,d,ab$ and $m.$ I think I can get you part way, but I have not dealt with all the cases. Given that the objective function ...
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### Constrained optimization of a sum

The problem $$\begin{array}{rcl} \min & \sum_{j=1}^n c_j x_j & \\ \mbox{st} & \sum_{j=1}^n x_j & = & b, \\ & l \leq x \leq u. & & \\ \end{array}$$ can ...
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### Finding the minima of a multivariable function with constraints

I'm not sure there is a way to guarantee a global optimum. If you are willing to settle for a local optimum, you could try a penalty method. For instance, you could square the difference between left ...
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1 vote

Assuming set $a=\{a_1,a_2,a_3\}$ is filled with variable $a_k$ and also where $a_j$ can take any value from set $a$, lets try: $\sum_{j=1}^3 a_j\cdot z_{j,i} = a_i \ \ \forall i$ $\sum_j z_{j,i} = ... • 3,343 1 vote ### Constrained optimization of a sum Primal Problem$\$\begin{align} \text{maximize} \quad & \sum_{i=1}^n c_i x_i \\\ \text{subject to} \quad & \sum_{i=1}^n x_i = 0 \\ & x_i \ge -1 \quad \forall i=1,\ldots,n \\ & x_i \le ...

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