We present a new class of algorithms for determining whether there exists a point x ɛ Rn satisfying the nonlinear inequality constraints ci(x) ≤ 0, i=1, …, m, subject perhaps to satisfying linear inequality constraints lj¬(x) ≤0, j=1, …,k which are known to be feasible. Our algorithm consists of solving a sequence of linearly constrained optimization problems, using a sequence of objective functions ф(x,p) which are at least twice continuously differentiable, and which are generated by monotonically increasing the value of the non-negative parameter p. It is shown that in almost all cases, once p reaches or exceeds some finite value, that the solution to the linearily constrained optimization problem either is a feasible point, or establishes the infeasibility of the set of constraints. Computational results are presented in which the algorithm performs satisfactorily on feasible and on infeasible systems.
Schnabel, Robert B., "Determining Feasibility of a Set of Nonlinear Inequality Constraints ; CU-CS-172-80" (1980). Computer Science Technical Reports. 170.