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A new approach for obtaining the second order sufficient conditions for nonlinear mathematical programming problems which makes use of second order derivative is presented. In the so-called second order -approximation method, an optimization problem associated with the original nonlinear programming problem is constructed that involves a second order -approximation of both the objective function and the constraint function constituting the original problem. The equivalence between the nonlinear...
By using some NCP functions, we reformulate the extended linear complementarity problem as a nonsmooth equation. Then we propose a self-adaptive trust region algorithm for solving this nonsmooth equation. The novelty of this method is that the trust region radius is controlled by the objective function value which can be adjusted automatically according to the algorithm. The global convergence is obtained under mild conditions and the local superlinear convergence rate is also established under...
In this paper we introduce a new smoothing function and show that it is coercive under suitable assumptions. Based on this new function, we propose a smoothing Newton method for solving the second-order cone complementarity problem (SOCCP). The proposed algorithm solves only one linear system of equations and performs only one line search at each iteration. It is shown that any accumulation point of the iteration sequence generated by the proposed algorithm is a solution to the SOCCP. Furthermore,...
The author investigates a Monte Carlo algorithm for finding suboptimal solutions for a wide clase of complicated optimization problems characterized by a large combinatorial complexity. This algorithm was applied to one specific problem: circular wheel balance optimization. The slow increase of the effort along with the increasing size of the problems and the generality of the method promise that the thermodynamically motivated optimization will become a very universal and effective optimization...
The article deals with certain nonconvex optimization problem which have features analogous to those of the linear optimization problems. We can find their absolute extrema and the set all optimal points of such nonconvex optimization problem represents the closure of a face of a spherical polyhedron which is its feasible set.
The relation between the general optimality conditions in terms of contact cones and the Kuhn-Tucker conditions in the special case of pseudo-convex and quasi-convex functions and their consequence to Lagrangian multipliers are given.
We consider the Airspace Sectorization Problem (ASP) in which airspace has to be partitioned into a given number of sectors, each of which being assigned to a team of air traffic controllers. The objective is to minimize the coordination workload between adjacent sectors while balancing the total workload of controllers. Many specific constraints, including both geometrical and aircraft related constraints are taken into account. The problem is solved in a constraint programming framework. Experimental...
We consider the Airspace Sectorization Problem (ASP) in which airspace
has to be partitioned into a given number of sectors, each of which
being assigned to a team of air traffic controllers. The objective is
to minimize the coordination workload between adjacent sectors while
balancing the total workload of controllers. Many specific
constraints, including both geometrical and aircraft related
constraints are taken into account. The problem is solved in a
constraint programming framework. Experimental...
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