Conjugate points for a constrained nonlinear programming problem
In a former paper by the author, the notion of conjugate point for unconstrained finite dimensional optimization problems was introduced. This notion is based on the discretized version of the Jacobi equation related to the second-order Hessian matrix of the objective function. The aim of this paper is to extend this theory to the inequality-equality constrained situation and offer necessary and sufficient conditions of optimality for such programming problems. As an illustration, the finite-dimensional version of the shortest path problem on the unit sphere is analyzed.
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