Deterministic global optimization of mixed-integer nonlinear programs (MINLP) is broadly applicable in diverse domains ranging from molecular biology to refinery operations to computational chemistry to synthesizing sustainable processes. MINLP is mathematically defined:

where C, B, I, and M represent the number of continuous variables, binary variables, integer variables, and constraints, respectively. Parameter vectors **b _{m}^{LO}** and

**b**bound the constraints. We assume that it is possible to infer finite bounds [

_{m}^{UP}**x**, x

_{i}^{L}_{i}

^{U}] on the variables participating in nonlinear terms f

_{m}and that the image of f

_{m}is finite on

**x**. Typical expressions for f

_{0}(

**x**,

**y**,

**z**) and f

_{m}(

**x**,

**y**,

**z**) are:

where the powers p_{sm, c} are constant reals; c_{m}, a_{m}, Q_{m}, c_{sm}, c_{em}, c_{lm} are constant coefficients; S_{m}, E_{m}, L_{m} are the number of signomial, exponential, and logarithmic terms, respectively.

**ANTIGONE** (Algorithms for coNTinuous / Integer Global Optimization of Nonlinear Equations) is a computational framework for globally solving mixed-integer nonlinear optimization problems. **ANTIGONE** is available through Princeton University and GAMS (beginning distribution 24.1).

The aggregate performance profiles [Dolan and Moré; PTOOLS] for the complete test suite diagrammed in the figures display a strong advantage for **ANTIGONE** on 2571 test cases across a wide array of problem classes:

Time | Percent gap remaining |

**ANTIGONE** is the fastest solver for ≈ 41% of the test cases and
can address ≈ 60% of the test cases within the time limit.
Additionally, **ANTIGONE** generally closes more of the optimality gap. The success of **ANTIGONE** is a direct result of finding and exploiting an array of special structure components within MINLP.