The aggregate constraint homotopy method for nonconvex nonlinear programming

An aggregate deformation homotopy method for min-max-min problems with max-min constraints

“…In many interior point methods for nonlinear programming problem such as the methods listed in [2,50,51], it's essential to assume that the feasible set is bounded or the iteration point sequences keep bounded. In [47], B. Yu et al discussed the convergence of the combined homotopy method in an unbounded feasible set.…”

“…Li in [21] and was sometimes referred to as an exponential penalty item (see [19]). Because of its good approximation property to the max-function, it was used extensively for many problems such as the nonlinear programming problem [21,22,51], the non-smooth min-max problem [23,24,36,48], variational inequalities [27], generalized complementarity problems [8,34,37], mathematical programm with equilibrium constraints (MPEC) [4] etc.…”

“…In [51], an aggregate homotopy method for a non-convex programming problem with inequality constraints was presented by utilizing the aggregate function smoothing the unified single max-type inequality constraint. In [27,28,52], the method was extended to the constrained sequential max-min problems, where the CM 3 P in this paper was seen as a special case and considered.…”

A modified constraint shifting homotopy method for solving general nonlinear multiobjective programming

“…But, this method still requires a strictly feasible initial point, so it is not convenient to implement. To relax the limitation of the strictly feasible initial point, Yu and Shang [26] presented a constraint shifting homotopy method for solving nonlinear programming with only inequality constraints. In 2009, Pérez et al [14] solved homotopy curve tracking optimization problems in the general case of an infeasible starting point through controlling the relaxation of the constraints.…”

Linear Evolutionary Algorithm

“…There are many solutions in literature, such as gradient projection method [1-3], Lagrangian and augmented Lagrangian penalty methods [4][5][6], and aggregate constraint method [7][8][9]. Among these methods, penalty function method is an important approach to solve global optimization problems.. To obtain the optimal solution of the original problem, the first step is to convert the optimization problem into an unconstrained optimization problem with a certain penalty function (such as Lagrangian multiplier).…”