The field of constrained optimization and neural networks is moving towards more efficient and scalable solutions. Recent developments have focused on integrating neural networks with traditional optimization techniques to improve performance and handle complex constraints. One notable direction is the use of neural networks to certify nonnegativity of polynomials, which has applications in non-convex optimization and control. Another area of research is the development of robust optimization frameworks that incorporate domain-consistent constraints, which has shown promise in reducing CO2 emissions in gas power plants. Noteworthy papers include:

• Neural Sum-of-Squares, which introduces a learning-augmented algorithm to certify the SOS criterion, achieving speedups of over 100x compared to state-of-the-art solvers.
• Neural Network-enabled Domain-consistent Robust Optimisation, which delivers domain-consistent robust optimal solutions that achieve a verified 0.76 percentage point mean improvement in energy efficiency.
• Optimization Modulo Integer Linear-Exponential Programs, which establishes the complexity of the optimization problem for integer linear-exponential programs and provides an algorithm to determine whether an integer linear-exponential straight-line program encodes a solution.