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1 answer

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 simply done by applying $C \geqslant c_1$, and $C…
Mostafa
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Prove that these linear programming problems are bounded by $O(k^{1/2})$

Prove that these linear programming problems are bounded by $O(k^{1/2})$ Conjecturally the expanded partial sums of the Möbius transform of the Harmonic numbers have two out of three properties in common with this set of linear programming…
Mats Granvik
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2 answers

Branching rules in commercial MIP solvers

I am working on a branch-and-cut algorithm, and I have spent quite some effort into improving the branching decisions that are made by commercial solvers, such as CPLEX and Gurobi. However, it was never successful: the standard branching by Cplex…
Albert Schrotenboer
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16
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3 answers

How to model nonlinear regression?

As part of my research in statistics, I recently stumbled upon this paper1 which provides an operational perspective into linear models. In simple linear regression, quadratic programming can be used to solve the problem where for least squares, the…
16
votes
3 answers

How to take the dual of a conic optimization problem?

Given a conic problem $$\min \{c^\top x \mid Ax \succeq_\mathit{C} b\}$$ for an arbitrary cone $C$, how can I construct the dual to the problem? Moreover, in Linear Programming one constructs the dual with the intention of finding a valid (in fact…
YukiJ
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16
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7 answers

Does there exist an aggregation of videos on optimization?

Is there a website or otherwise maintained list of talks regarding mathematical optimization? This would be a big help for the community it seems. I'm most interested in those relating to integer programming.
user3235
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2 answers

Is the Irreducible Infeasible Subset (IIS) of an LP unique?

The IIS is a standard part of most modern solvers, but is it unique for an LP? My intuition tells me that it should be, but I could find any proof.
Richard
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2 answers

Why do we need to measure the difficulty of mixed-integer programming problems?

I'm doing a project about the estimation of the difficulty of mixed-integer programming problems. The MIP instances are from MIPLIB 2017. And there are three categories of MIPs provided by MIPLIB 2017, which are "Easy", "Hard" and "Open", which…
Karen Jin
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16
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3 answers

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

Are there any books on Operations Research subjects by world-famous authors which have been made available for free access on the web, despite never having been "completed" to the standard to which the authors aspired? I would also accept completed…
Mark L. Stone
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16
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4 answers

Branch and Bound Implementation

Branch and Bound (B&B) is a general solution approach to solve combinatorial optimisation problems. I was wondering how B&B is implemented in practice. Although it may be relevant, but I am not looking for an explanation of why/how B&B works.…
rasul
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4 answers

What are the most-used technical skills in OR?

Apart from: modeling, "coding" the model and using an open source/commercial solver Implementing an approximation method (metaheuristics, greedy, etc.) Implementing exact methods (dynamic programming, specific algorithms like network flows, etc)…
Joffrey L.
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1 answer

What Is OR Research Like?

I am working on my MSc thesis right now which is in resource economics, but I have ended up actually operating mostly in the realm of OR and learning about programming, algorithms, optimization problems, some complexity theory, and a bit of machine…
GrayLiterature
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1 answer

IPOPT with HSL vs MUMPS

What are the advantages (if any) of using IPOPT with HSL vs MUMPS? HSL has a reputation of being faster, but does it walk the walk? In particular, does HSL scale better for large-scale problems? We have been using IPOPT with MUMPS in our engine and…
Nikos Kazazakis
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1 answer

Convexity of Variance Minimization

$X$ is a discrete random variable taking value $x_n$ with probability $1/N$ for $n=1, \ldots,N$. I would like to set the $x_n$ values in an optimization problem. My objective is to minimize the variance while satisfying a set of constraints. So the…
independentvariable
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3 answers

Benchmark problems for scenario-based stochastic optimization

$\newcommand{\E}{\mathbb{E}}$I am working on numerical algorithms for solving convex large-scale multistage scenario-based problems and I am looking for some standard benchmarks problems. I have so far worked with scenario trees generated from data,…