# Questions tagged [nonlinear-programming]

For questions about mathematical optimization problems involving a nonlinear objective function and/or nonlinear constraints.

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### How to formulate (linearize) a maximum function in a constraint?

How to formulate (linearize) a maximum function in a constraint? Suppose $C = \max \{c_1, c_2\}$, where both $c_1$ and $c_2$ are variables. If the objective function is minimizing $C$, then it can be ...
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### Optimization Problem Libraries

Can someone please make a list of optimization problem libraries so that the community can add to and refine it? I know a few off the top of my head.
913 views

### CPLEX non-convex Quadratic Programming algorithms

CPLEX solves non-convex quadratic problems to global optimality with a global optimality option (in version 12). The relevant pages are this and this. I benchmarked many solvers, and see that CPLEX ...
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### How to linearize the product of two continuous variables?

Suppose we have two variables $x, y \in \mathbb R$. How can we linearize the product $xy$? If this cannot be done exactly, is there a way to get an approximate result?
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### Linearize or approximate a square root constraint

I encounter a nonlinear constraint that contains the square root of a sum of integer variables. Of course one could use nonlinear solvers and techniques; but I like linear programming. Are there any ...
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### Cubic programming and beyond?

It is almost inevitable in Operations Research to come across linear or quadratic programming problems. The overall structures of these problems are below: \begin{align}\begin{array}{ll} \sf{Linear}\\ ...
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### Are metaheuristics ever practical for continuous optimization?

All of the applications of metaheuristics that I can think of are for discrete optimization (usually combinatorial optimization) problems. Are metaheuristics ever practical tools for continuous ...
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### Expressing an implication as ILP where each implication term comprises a chain of boolean ORs

Consider an implication of the form $A \implies B$ where both $A, B$ comprises a chain of Boolean OR variables. For example, $(a_1 \lor a_2 \lor a_3) \implies (b_1 \lor b_2 \lor b_3)$. How can this ...
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### Can Gurobi or CPLEX handle nonlinearly constrained problems?

Though my title is quite general (please feel free to edit), indeed, I wonder if the following models can be solved in Gurobi or CPLEX. Model 2 is just an alternative one to Model 1. Although we ...
Now, for each system $X$ $(X=A,B,C,E)$, my objective is $$\max\min\frac{s_{x_u}}{d_{x_u}}$$ here, $x=a$ for system A, $x=b$ for system B and follows... and for the whole system, my objective is \max\...
I have the following objective function. The variables: $h_p$, $e_{trs}\left(h_p\right), w_{trs}\left(h_p\right)$ are all non-negative continuous. $T,R,S,\pi_{trs}$ are polynomially-sized sets. All ...