solveurs

Solveurs, or solvers, are software tools designed to find solutions to mathematical problems, equations, constraints, or optimization tasks. Depending on the problem, a solveur may return a feasible solution, an optimal solution, or a proof of infeasibility. Solveurs can operate numerically, symbolically, or logically, and they may provide exact results or approximate results within user-specified tolerances.

Common categories include numeric solvers, optimization solvers, constraint solvers, and logical solvers. Numeric solvers handle systems of linear or nonlinear equations and differential equations. Optimization solvers aim to maximize or minimize an objective function under constraints, covering linear programming (LP), mixed-integer programming (MIP), and nonlinear programming (NLP). Constraint solvers address combinatorial or discrete constraints, solving constraint satisfaction problems (CSPs). SAT solvers determine the satisfiability of propositional formulas, while SMT solvers extend this to theories such as arithmetic. Symbolic solvers manipulate mathematical expressions algebraically to perform simplification, solving, or transformation.

Input formats and interfaces vary by category. LP formats (such as LP or MPS), CNF for SAT, and SMT-LIB for SMT-solvers are common standard representations. Solvers are typically accessed through APIs, modeling languages, or integration into larger software pipelines. Popular examples include commercial and open-source options across categories, such as linear and mixed-integer solvers, SAT/SMT solvers, and specialized numerical or symbolic tools.

Applications span engineering, operations research, computer science, AI planning, verification, and design automation. Choosing a solveur involves considering problem structure, required guarantees (feasibility, optimality, proofs), computational scalability, and ease of integration.