Welcome to Quantified Programming!

Quantified (mixed) integer programming is an extension of (mixed) integer linear programming where the variables are ordered explicitly and some variables are existentially and others are universally quantified. They can be interpreted as multistage optimization problems under uncertainty or as two-person zero-sum games between an existential and a universal (or adversarial) player. Solutions are so called winning strategies for the existential player that specify how to react on moves – certain fixations of universally quantified variables – of the universal player to certainly win the game. Our open source solver Yasol combines linear programming techniques with solution techniques from game-tree search and is able to solve multistage robust discrete optimization problems with mixed-integer recourse actions in the final decision stage. On this website we provide: