• 대한수학회지
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• 제40권2호
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• pp.287-305
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• 2003

Second order necessary optimality condition for properly efficient solutions of a twice differentiable vector optimization problem is given. We obtain a nonsmooth version of the second order necessary optimality condition for properly efficient solutions of a nondifferentiable vector optimization problem. Furthermore, we prove a second order necessary optimality condition for weakly efficient solutions of a nondifferentiable vector optimization problem.

• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.981-1000
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• 2009

This paper considers asset liability management problems when their deterministic equivalent formulations are general nonlinear optimization problems. The presented approach uses a nonmonotone trust region strategy for solving a sequence of unconstrained subproblems parameterized by a scalar parameter. The objective function of each unconstrained subproblem is an augmented penalty-barrier function that involves both primal and dual variables. Each subproblem is solved approximately. The algorithm does not restrict a monotonic decrease of the objective function value at each iteration. If a trial step is not accepted, the algorithm performs a non monotone line search to find a new acceptable point instead of resolving the subproblem. We prove that the algorithm globally converges to a point satisfying the second-order necessary optimality conditions.