Exact: algorithm will eventually provide a provably optimal solution. Approximate: algorithm will eventually produce a solution with some guarantees (e.g. a tour being at most twice as long as the ...

Two open problems in linear optimization (which is considered more or less a 'solved' subfield by many): Is there a pivoting strategy for the Simplex algorithm guaranteeing to find an optimal vertex ...

You should take a look at GCG, a plugin for SCIP and part of the SCIP Optimization Suite. After the standard presolving process of SCIP, GCG performs a Dantzig-Wolfe decomposition of the problem to ...

Mittelmann benchmarks a number of (LP-)Solvers, some of which are open source. A recent new open source solver is HiGHS.

Let's start with the easy one: Ellipsoid Method Never use it. Even though it might appear efficient in the complexity-theory sense, it performs terrible and suffers heavily from numerical issues. ...

Google Hashcode had some optimization challenges in the past. Problem definitions and data from previous years can be found here.

First of all, usually implementations are centered around the revised dual simplex, not the primal (even though solvers will still use a primal simplex method implementation for some tasks in the ...

There are multiple aspects to this topic. What can be done by testset compilers to prevent finetuning? For one, testset creators are usually not including many very similar problems into the ...

Counterexamples to your arguments: Argument 1: Only affine equality constraints are convex, $x = y^2$ is not convex. Argument 3: Take $f(x) = x^4$ and $g(x) = x$. Both are convex, but the ratio $h(x)... View answer Accepted answer 12 votes SCIP does not currently support any trigonometric functions as of this post from May 2018. COUENNE appears to handle$\sin$and$\cos$expressions. ANTIGONE appears to not support any trigonometric ... View answer Accepted answer 8 votes Not an expert on simplex, but here's my attempt on an answer: In general, the solution of the (previous) LP Relaxation will no longer be primal feasible when the primal LP is tightened (e.g. new cut ... View answer 7 votes While this class of problems is still hard to solve (see the other answers for details), one speciality is that it has a trivial feasible solution$x=0$, which is not the case in general integer ... View answer 7 votes The act of moving soft constraint into the objective function using penalties is closely related to Lagrangian Relaxation and Lagrangian Multipliers. The method penalizes violations of [...] ... View answer 6 votes I mostly agree with Marco Lübbecke. I would like to add that "vectors of the right dimension" are sometimes called solution candidates. Also when we refer to an "infeasible solution" we often mean ... View answer 5 votes Another paradigm to parallelize search heuristics is the Backbone strategy. See for example this paper. The main idea is to run multiple instances of an arbitrary heuristic in parallel, and then ... View answer 3 votes You only specified$x$is "continuous". I'll interpret this as$x\$ is rational rather than real. This is not a terrible assumption, as floating point numbers in computers are rational anyways. A ...