Developing deterministic algorithms for solving virtually all nonlinear optimization problems

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Due to powerful solvers, a variety of large-scale optimization problems can be solved in a small amount of time. Nonlinear optimization problems are, however, excluded from this benefit, especially when the convexity is not assumed. In this research, we paid attention to the fact that almost all nonlinear optimization problems can be formulated into a class of problems of minimizing a concave function over a convex set, and developed some deterministic algorithms for solving it. We verified that each of them converges in theory to an optimal solution, and that it actually terminates in a practical amount of time on a computer.