# Tag Info

Accepted

### Optimization Problem Libraries

Quadratic assignment problem Vehicle routing problem also at HEC Traveling salesman Graph partitioning Quantified Boolean formulas Constraint solvers Shortest paths Mixed integer programming Train ...
• 2,745
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### How to formulate (linearize) a maximum function in a constraint?

(I'm going to change $c$ to $x$ in my answer, since $c$ is usually used for cost coefficients, not decision variables.) We want a set of constraints that enforces $X = \max\{x_1,x_2\}$. Define a new ...
• 13.1k

### Optimization Problem Libraries

Here is a start. Please add to this. BOLIB: Bilevel Optimization LIBrary of Test Problems https://bobilib.org/ and https://eprints.soton.ac.uk/436854/1/BOLIBver2.pdf CBLIB: The Conic Benchmark ...
• 13.5k
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### Deep Reinforcement Learning for General Purpose Optimization

"General purpose optimization" is quite broad, so I'll take a step back first, to better identifying the motivation of using ML in optimization settings. To keep things simple, I'll consider ...
• 4,218
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### Cubic programming and beyond?

In addition to the excellent answers that are already posted, I want to add that for the pragmatic optimizer, quadratic may already be sufficient. For example, the cubic constraint $x^3 \le x$ may be ...
• 6,252
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### Linearize or approximate a square root constraint

This can be handled as an MISOCP, Mixed-Integer Second Order Cone problem. The leading commercial MILP solvers can also handle MISOCP. Specifically, due to $x_{ij}$ being binary, $x_{ij}^2 = x_{ij}$. ...
• 13.5k
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### Trustful Nonlinear Programming

Local nonlinear optimization solvers, such as IPOPT, are not guaranteed to find a feasible point for problems that are feasible. That is certainly the case for problems with non-convex constraints, ...
• 13.5k

### Cubic programming and beyond?

I am not sure whether you are looking for polynomial optimization like Introduction to concepts and advances in polynomial optimization by Martin Mevissen, or polynomial optimization by Hoang Tuy?
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### Nonlinear integer (0/1) programming solver

Option 1: Submit as is to a solver which can globally optimize MIQPs having non-convex objective, and which might reformulate to a linearized MILP model under the hood. Such solvers include CPLEX, ...
• 13.5k
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### Sum of Max terms maximization

If your problem is reasonably small then one relatively simple approach is to reformulate the objective as a MIP, under a big-M assumption. Suppose that our objective is to maximize $$\sum_i g_i(x),$$...
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• 2,745
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### IPOPT with HSL vs MUMPS

This question happened to appear only a couple days after Byron Tasseff, Carleton Coffrin, Andreas Wächter, and Carl Laird (the last two are the original authors of IPOPT together with Larry Biegler) ...
• 1,095
Accepted

While iteratively approximately solving the first order Karush-Kuhn-Tucker conditions, many (nonconvex) nonlinear solvers "roll downhill", i.e., enforce descent (for minimization) of the objective ...
• 13.5k
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### Can Tuning Knitro Solver Considerably Make A Difference?

(Disclaimer: I am a developer of Knitro) When developing a NLP solver, we set the default values for the different options so as to minimize the resolution time in average for different class of ...
• 1,511

### Optimization Problem Libraries

Some more: Atamturk datasets on fixed-charge flow, lot sizing, mixed-integer knapsack, and more Combinatorial Auction Test Suite (CATS) National Traveling Salesman Problems VLSI data sets: Another ...
• 5,874

### Cubic programming and beyond?

Thanks to everyone who answered this question for introducing the concept of polynomial programming. From there I have found two papers that link cubic programming to convex programming, and provide ...
• 5,442