The field of discrete optimization is moving towards a deeper understanding of the structural parameters that govern the complexity of problems. Recent research has highlighted the importance of rank as a key parameter in discrete optimization, analogous to treewidth in algorithmic graph theory. This has led to the development of new exact algorithms for problems such as quadratic unconstrained binary optimization (QUBO) and its cardinality-constrained extension. Additionally, there is a growing interest in the study of lexicographic cost functions and their impact on the complexity of optimization problems. In computational algebra, researchers are exploring the connections between optimization problems and Hilbert's Nullstellensatz, a fundamental problem in algebraic geometry. This has led to a better understanding of the complexity of problems such as the Affine Polynomial Projection Problem and the Sparse Shift Problem. Noteworthy papers in this area include: Affine Predicate Geometry: A Courcelle-Type Metatheorem for Rank-Bounded Pseudo-Boolean Optimization, which establishes rank as a structural parameter for discrete optimization. A Quantum-Inspired Algorithm for Solving Sudoku Puzzles and the MaxCut Problem, which proposes a quantum-inspired algorithm for solving QUBO problems. Problems from Optimization and Computational Algebra Equivalent to Hilbert's Nullstellensatz, which shows that many important problems from optimization and algebra are complete or hard for the complexity class associated with Hilbert's Nullstellensatz.