# Problem Formulation

**Download the updated Challenge 3 Problem Formulation document dated May 15, 2023. **Constraint relaxation penalties are now required to be strictly positive. Strict inequalities are used in Eqs. (280) to (291).

The Change Log (section 8) lists the major changes since the original was posted.

The original version had multi-mode devices, which were conceived of as a means for modeling combined cycle generators and storage devices. In the current version of the formulation, multi-mode devices have been removed. Combined cycle generators, storage devices, and multi-mode devices may be added to future Challenges.

The previous Challenge 3 Problem Formulation document dated January 26, 2023 is still available.

The previous Challenge 3 Problem Formulation document dated January 13, 2023 is still available.

The previous Challenge 3 Problem Formulation document dated January 6, 2023 is still available.

The previous Challenge 3 Problem Formulation document dated July 1, 2022 is still available.

The original Challenge 3 Problem Formulation document dated February 16, 2022 is still available.