# 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 isnĀ“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 ...
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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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### Solve nonlinear programming problems practically

A common and free NLP solver is IPOPT. IPOPT implements an interior-point line-search filter method, a variation of the interior-point method, these interior point method uses the barrier functions ...
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### MINLP involving integrals, sparse matrices and CDF of random variables. Best environment?

So it seems your strategy (enumerative search on the integer variables) works well, and the issue is solving pure NLP problems. The choice of programming/modeling language you use is dependent on what ...
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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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1 vote

### Efficient Algorithm for Scheduling 140 Predefined 1:1 Meetings with Variable Participant Constraints Over 7 Slots?

You could also use a MIP. Here's an example using JuMP and HiGHS: ...
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### Efficient Algorithm for Scheduling 140 Predefined 1:1 Meetings with Variable Participant Constraints Over 7 Slots?

With 1:1 meetings only, this is a classical application of graph coloring. The graph has a node for each person and an edge for each required meeting. The edge colors correspond to time slots, and ...
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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: $\sum_{j=1}^3 a_j\cdot z_{j,i} = a_i \ \ \forall i$ $\sum_j z_{j,i} = ... • 3,485 1 vote ### Constrained optimization of a sum Primal Problem$\$\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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