Stochastic global optimization methods. part 11: multi level methods
Mathematical Programming: Series A and B
Integer and combinatorial optimization
Integer and combinatorial optimization
Zero duality gap for a class of nonconvex optimization problems
Journal of Optimization Theory and Applications
Convexification of a noninferior frontier
Journal of Optimization Theory and Applications
Hidden convexity in some nonconvex quadratically constrained quadratic programming
Mathematical Programming: Series A and B
Second-order global optimality conditions for convex composite optimization
Mathematical Programming: Series A and B
Convexification of a noninferior frontier
Journal of Optimization Theory and Applications
Decreasing Functions with Applications to Penalization
SIAM Journal on Optimization
Approximate Optimal Solutions and Nonlinear Lagrangian Functions*
Journal of Global Optimization
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In this paper a successive optimization method for solving inequality constrained optimization problems is introduced via a parametric monotone composition reformulation. The global optimal value of the original constrained optimization problem is shown to be the least root of the optimal value function of an auxiliary parametric optimization problem, thus can be found via a bisection method. The parametric optimization subproblem is formulated in such a way that it is a one-parameter problem and its value function is a monotone composition function with respect to the original objective function and the constraints. Various forms can be taken in the parametric optimization problem in accordance with a special structure of the original optimization problem, and in some cases, the parametric optimization problems are convex composite ones. Finally, the parametric monotone composite reformulation is applied to study local optimality.