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5 votes

Nonlinear optimization with constraint involving long product of optimization variables

You are repeating the same expressions over and over again. It may be worthwhile to see if it is better to define: $$y_j = \begin{cases}y_{j-1}\cdot x_j & \text{for $j\gt 3$}\\ x_j & \text{...
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3 votes

Geometric Programming with Simple Affine Equality Constraint

You might be able to use the suggestions in https://docs.mosek.com/modeling-cookbook/expo.html#geometric-programming to convert your problem to a conic optimization problem. It might also make it ...
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3 votes

Np-hard sequencing or packing problems with total ordering between elements

Scheduling problems requiring a total ordering of the tasks are generally called sequencing problems in the OR literature. Car sequencing is one of the most famous ones. The car sequencing problem is ...
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5 votes

Linearize function

One approach is to perform the usual linearization of a product of a bounded variable and a binary variable, by introducing a new variable to represent the product, along with additional linear ...
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1 vote
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Optimization software for real-valued functions/constraints of complex arguments

I sat down and worked a bit on this. Since I am only interested in the magnitude of the polynomial it might be helpful to employ the polar representation, i.e., $1 - z_j \lambda = r_j e^{i\phi_j}$. ...
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  • 231
1 vote

Can Expected value of perfect information be zero?

EVPI needs to be nonnegative; it does not need to be strictly positive. Suppose, for example, that you have an LP model with three scenarios. The variable vector is $x$, the constraints are identical ...
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1 vote

calculations after the docplex solution

With docplex as with other cplex API you can do postprocess. For instance, in the zoo example ...
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1 vote

When was the exploration and exploitation tradeoff first mentioned in literature?

With reference to the paper in the original post "Exploration and Exploitation in Organizational Learning" (E&E) by James G. March, the paper "The Lost Experiment in Exploration and ...
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  • 131
5 votes
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Correct way to add slack variables to model

You can add slacks to whatever combination of constraints you want. But any constraint not having a slack must be satisfiable in its "no slack" form, else the model will be infeasible. And ...
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2 votes

Adding cuts doesn't change the solution of master problem in Benders decomposition

Suppose that the master problem entails maximizing a variable $z$, and let $x$ be the master problem variables. Somewhere along the line, the solver arrives at a solution $(\bar{x}, \bar{z})$ which is ...
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3 votes
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Adding cuts doesn't change the solution of master problem in Benders decomposition

You can certainly get the same master objective value after adding optimality cuts, but you should not get the same solution in consecutive master solver calls until the final iteration, when the ...
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2 votes

Unbounded master problem in Benders decomposition

RobPratt's and prubin's answer indeed solves the problem in the post. If someone wonders whether there exist other solutions, I found a class of stabilization methods in Frangioni, A. (2020) for ...
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5 votes

Unbounded master problem in Benders decomposition

Yes, it is possible in theory. An alternative to bounding the objective function is bounding the variables. If this is a "real-world" model (where the variables represent actual decisions), ...
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7 votes
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Unbounded master problem in Benders decomposition

Assuming your master problem is to minimize $\eta$, a simple way to avoid unboundedness, even before adding any cuts, is to impose a redundant lower bound $\eta \ge L$ for some constant $L$. Often, ...
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5 votes
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large scale optimization with Python

Quadratic programming solvers in Python with a unified API (here) includes most of the quadratic programming solvers such as CVXOPT (can take advantage of sparsity), Gurobi, MOSEK, OSQP, etc. The ...
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