Mark L. Stone
  • Member for 2 years, 8 months
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  • Nonlinear Multivariate Dynamic Stochastic Global Optimum
OR Software Forums
27 votes

Here is the augmented and updated list. This should be a good starting point for further improvements. This list is very optimization-heavy (even the automatic differentiation software is most likely ...

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Optimization Problem Libraries
25 votes

Here is a start. Please add to this. BOLIB: Bilevel Optimization LIBrary of Test Problems https://eprints.soton.ac.uk/436854/1/BOLIBver2.pdf CBLIB: The Conic Benchmark Library: http://cblib.zib.de/ . ...

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How Close Is Linear Programming Class to What Solvers Actually Implement for Pivot Algorithms
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21 votes

There was an excellent lecture by Bob Bixby in 2015 at the Zuse Institute Berlin (ZIB) as part of Combinatorial Optimization at Work 2015. Bixby founded CPLEX and Gurobi, 2 of the 3 leading commercial ...

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Linearize or approximate a square root constraint
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20 votes

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, $x_{ij}^2 = x_{ij}$. ...

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Trustful Nonlinear Programming
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18 votes

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, ...

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Is This Constraint Convex?
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18 votes

Arguments 3 and 4 are incorrect. The Right-Hand Side (RHS) is not convex. Even if it were, setting a nonlinear equality with either side non-affine is non-convex. As the final coup de grace, even if ...

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When to use indicator constraints versus big-M approaches in solving (mixed-)integer programs
18 votes

Here is the advice in the IBM CPLEX documentation. So this pertains to CPLEX. I don't know to what extent it applies to other solvers. First of all, indicator constraints may not be available in all ...

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Single reference for Mixed Integer Programming formulations to linearize, handle logical constraints and disjunctive constraints, do Big M, etc?
17 votes

Here is a nice, succinct,and easy to understand reference for how to do all this and more. Answers to many future questions can be handled by referencing the appropriate section number in this ...

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Nonlinear integer (0/1) programming solver
16 votes

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, ...

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Does the problem of P vs NP come under the category of Operational Research?
16 votes

P vs. NP may come "under" the category of Operational Research (O.R.). But unlike theoretical computer science and algorithm analysis, in which P vs. NP may be a be all and end all, practical (non-...

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Reference for "expectation preserves convexity"
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16 votes

Reference "Convex Optimization" by Boyd and Vandenberghe https://web.stanford.edu/~boyd/cvxbook/, section 3.2.1, p. 79. These properties extend to infinite sums and integrals. For example if $f(x,...

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Well-known parent/child pairs in the field of OR
15 votes

John D.C. Little, of $L = \lambda W$ fame : father John N. "Jack" Little https://en.wikipedia.org/wiki/John_N._Little and https://www.mathworks.com/company/aboutus/founders/jacklittle.html, President ...

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Are there Operations Research books by world-famous authors made available on the web?
13 votes

Just posted on January 16, 2020: Elements of Scheduling, collected and edited by Jan Karel Lenstra and David B. Shmoys This {pdf file} presents the fragments of a book on machine scheduling. Work on ...

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Does it make sense to use strict equality constraints in optimization?
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13 votes

I suspect you read that actual floating point optimization solvers treat strict inequalities ($<$ and $>$) as non-strict inequalities ($\le$ and $\ge$). Solvers also give themselves a fudge ...

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Classics in Operations Research from around WW II?
13 votes

THE classic book on WW II Operations Research is "Methods of Operations Research" by Philip M. Morse, George E. Kimball. It is basically WW II O.R., less classified material. The Dover Press version ...

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What are the reasons OR industry projects fail?
12 votes

This may or may not be considered as occurring only within an OR context, but not getting senior-enough leadership guidance and buy-in on the client side (whether internal or external) as to the need ...

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Solvers and saddle points
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12 votes

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 ...

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CPLEX non-convex Quadratic Programming algorithms
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12 votes

The best publicly available CPLEX global QP algorithm description I am aware of is the tutorial presentation by Ed Klotz of IBM at the March 2018 INFORMS Optimization conference. Performance Tuning ...

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Cubic programming and beyond?
12 votes

+1 for @MarcoLübbecke But in addition, this is also known as "Polynomial Programming". Also look at algebraic geometry and semialgebraic sets, and sum of squares optimization: Wikipedia and Lall, ...

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Working with absolute values in constraint in a LP or MILP
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12 votes

You need to model disjunctive constraints. I will assume that variable $x$ is constrained to lie in $L_1 \le x \le U_1$ or $L_2 \le x \le U_2$. For instance, if you have the constraint $2 \le |x| \...

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Is a mathematical programming problem with no objective function an optimization problem?
11 votes

Yes. But some software may require explicit specification of an objective, which can be a constant. Yes. An optimization solver will attempt to find a feasible solution. Any feasible solution is ...

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How to run MOSEK solver in CVXOPT
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10 votes

As determined in the comment exchange to the question, because the matrix P has minimum eigenvalue which is negative, it is not positive semidefinite, and therefore it is a non-convex problem. ...

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How can I identify the reason that makes a MILP model hard for solvers such as CPLEX?
10 votes

MILPs are NP-hard. People make a big deal about NP-hardness for a reason - in the worst case they are very, very hard to solve. There is a short, easy to understand exposition of this by @Johan ...

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Debugging cplex model
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10 votes

CPLEX has a conflict refiner. The instructions for invoking it are at How to invoke the conflict refiner.

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"Best practices" for formulating MIPs
10 votes

Perhaps you are only talking about MILPs, but you don't say, so I will say something of interest for MINLPs. Regarding point 1: Suppose your model has a convex nonlinear inequality constraint, $f(x) ...

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When to use indicator constraints versus big-M approaches in solving (mixed-)integer programs
10 votes

Question by me at the IBM CPLEX Forum: Are indicator constraints immune to trickle flow or other numerics-induced logic "errors"? Are indicator constraints immune to trickle flow or other ...

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How to model nonlinear regression?
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10 votes

NEOS has a nice web page on nonlinear least squares. It contains several classic (i.e., not so new, but still good) references for nonlinear least squares. There is a very nice introduction to the ...

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Significant bias introduced into simple simulation
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9 votes

You have fallen victim to the renewal paradox, a.k.a. inspection paradox, a.k.a. length-biased sampling. $F_{\Delta}$ is the distribution of service time for the kth customer, but it is NOT the ...

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Recommendations for OR video channels (YouTube etc.)
9 votes

Here are some YouTube channels having research level talks, all of which were livestreamed with live Q&A prior to being archived. These are all ongoing series with new talks (videos) added ...

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Which Python package is suitable for multiobjective optimization
9 votes

If @dbasson 's excellent answer is not what you're looking for, may I suggest the possibility of using multiobjective optimization capabilities in CPLEX or Gurobi (under Python)? CPLEX New ...

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