QPLIB

A Library of Quadratic Programming Instances

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The following diagrams provide aggregated statistics on sources and characteristics of the instances in QPLIB. You can download the raw data in csv format. The data fields are defined in the documentation.

Problem types

For a definition of the three letter problem classification see the documentation.
Continuous Instances /

Discrete Instances

CCB 3

CCL 16

CCQ 11

LCC 13

LCQ 52

QCC 3

QCL 6

QCQ 30

total 134

convex 32

non-convex 102

CBL 5

CML 12

CMQ 6

LBQ 9

LGQ 3

LIQ 2

LMC 14

LMQ 134

QBL 91

QBN 23

QBQ 5

QGQ 1

QIL 2

QML 11

QMQ 1

total 319

convex 31

non-convex 288

Variable types

Convexity

Left: Convexity of the continuous relaxation. Right: Fraction of problematic eigenvalues in the coefficient matrix of the objective function w.r.t. the total number of variables.

Problem sizes

See also the definition of nonzeros and nonlinear nonzeros in the documentation.

Density

In these scatter plots, each bubble represents an instance and the area of the bubble corresponds to the (nonlinear) density of the instance:

The density in left scatter plot is defined as (#nonzeros) / (#vars * (#cons + 1)).
The density in right scatter plot is defined as (#nonlinear nonzeros) / (#nonlinear vars * (#quadratic cons + 1 if objective is nonlinear)).
Densities below 0.05 are shown as 0.05.

The diagram below shows the instances with a quadratic objective function sorted according to the density of the quadratic objective function coefficient matrix.