Major applications of mixed-integer quadratically-constrained quadratic programs (MIQCQP) include quality blending in process networks, separating objects in computational geometry, and portfolio optimization in finance. Specific instantiations of MIQCQP in process networks optimization problems include: pooling problems, distillation sequences, wastewater treatment and total water systems, hybrid energy systems, heat exchanger networks, reactor-separator-recycle systems, separation systems, data reconciliation, batch processes, crude oil scheduling, and natural gas production. Computational geometry problems formulated as MIQCQP include: point packing, cutting convex shapes from rectangles, maximizing the area of a convex polygon, and chip layout and compaction. Portfolio optimization in financial engineering can also be formulated as MIQCQP. MIQCQP is mathematically defined:

where C, B, I, and M represent the number of continuous variables, binary variables, integer variables, and constraints, respectively. We assume that it is possible to infer finite bounds on the variables participating in nonlinear terms.

**GloMIQO** (Global Mixed-Integer Quadratic Optimizer; 1, 2) is a numerical solver addressing MIQCQP to ε-global optimality. **GloMIQO** is available through Princeton University and GAMS.

The aggregate performance profiles [Dolan and Moré] for the complete test suite diagrammed in the figures display a strong advantage for **GloMIQO** across a wide array of problem classes:

Time | Percent gap remaining |

**GloMIQO** is the fastest solver for ≈ 48% of the test cases and can address ≈ 70% of the test cases within the time limit. Additionally, **GloMIQO** generally closes more of the optimality gap. The success of **GloMIQO** is a direct result of finding and exploiting an array of special structure components within MIQCQP.