Multi-criteria test-suite minimization aims to remove redundant test cases from a test suite based on some criteria such as code coverage, while trying to optimally maintain the capability of the reduced suite based on other criteria such as fault-detection effectiveness. Existing techniques addressing this problem with integer linear programming claim to produce optimal solutions. However, the multi-criteria test-suite minimization problem is inherently nonlinear, due to the fact that test cases are often dependent on each other in terms of test-case criteria. In this paper, we propose a framework that formulates the multi-criteria test-suite minimization problem as an integer nonlinear programming problem. To solve this problem optimally, we programmatically transform this nonlinear problem into a linear one and then solve the problem using modern linear solvers. We have implemented our framework as a tool, called Nemo, that supports a number of modern linear and nonlinear solvers. We have evaluated Nemo with a publicly available dataset and minimization problems involving multiple criteria including statement coverage, fault-revealing capability, and test execution time. The experimental results show that Nemo can be used to efficiently find an optimal solution for multi-criteria test-suite minimization problems with modern solvers, and the optimal solutions outperform the suboptimal ones by up to 164.29% in terms of the criteria considered in the problem.