Semi-infinite minimax fractional programming problems with both inequality
and equality constraints are considered. The sets of parametric saddle point
conditions are established for a new class of nonconvex differentiable
semi-infinite minimax fractional programming problems under(?,?)-invexity
assumptions. With the reference to the said concept of generalized convexity,
we extend some results of saddle point criteria for a larger class of
nonconvex semi-infinite minimax fractional programming problems in comparison
to those ones previously established in the literature.
A new trust region method is presented, which combines nonmonotone line search technique, a self-adaptive update rule for the trust region radius, and the weighting technique for the ratio between the actual reduction and the predicted reduction. Under reasonable assumptions, the global convergence of the method is established for unconstrained nonconvex optimization. Numerical results show that the new method is efficient and robust for solving unconstrained optimization problems.
An ADMM-based SQP method for separably smooth nonconvex optimization