PIECEWISE LINEAR NCP FUNCTION FOR QP FREE FEASIBLE METHOD

In this paper, a QP-free feasible method with piecewise NCP functions is proposed for nonlinear inequality constrained optimization problems. The new NCP functions are piecewise linear-rational, regular pseudo-smooth and have nice properties. This method is based on the solutions of linear systems of equation reformulation of KKT optimality conditions, by using the piecewise NCP functions. This method is implementable and globally convergent without assuming the strict complementarity condition, the isolatedness of accumulation points. Purr thermore, the gradients of active constraints are not requested to be linearly independent. The submatrix which may be obtained by quasi-Newton methods, is not requested to be uniformly positive definite. Preliminary numerical results indicate that this new QP-free method is quite promising.

The Successive Approximation Broyden-like Algorithm for Nonlinear Complementarity Problems

In this paper, we present a new form of successive approximation Broyden-like algorithm for nonlinear complementarity problem based on its equivalent nonsmooth equations. Under suitable conditions, we get the global convergence on the algorithms. Some numerical results are also reported.

Smoothing Newton Algorithm for Nonlinear Complementarity Problem with a PFunction

By using a smoothing function,the P nonlinear complementarity problem(P NCP)can be reformulated as a parameterized smooth equation.A Newton method is proposed to solve this equation.The iteration sequence generated by the proposed algorithm is bounded and this algorithm is proved to be globally convergent under an assumption that the P NCP has a nonempty solution set.This assumption is weaker than the ones used in most existing smoothing algorithms.In particular,the solution obtained by the proposed algorithm is shown to be a maximally complementary solution of the P NCP without any additional assumption.

Superlinear Convergence of a Smooth Approximation Method for Mathematical Programs with Nonlinear Complementarity Constraints

Mathematical programs with complementarity constraints(MPCC) is an important subclass of MPEC.It is a natural way to solve MPCC by constructing a suitable approximation of the primal problem.In this paper,we propose a new smoothing method for MPCC by using the aggregation technique.A new SQP algorithm for solving the MPCC problem is presented.At each iteration,the master direction is computed by solving a quadratic program,and the revised direction for avoiding the Maratos effect is generated by an explicit formula.As the non-degeneracy condition holds and the smoothing parameter tends to zero,the proposed SQP algorithm converges globally to an S-stationary point of the MPEC problem,its convergence rate is superlinear.Some preliminary numerical results are reported.

Filter-sequence of quadratic programming method with nonlinear complementarity problem function

A mechanism for proving global convergence in filter-SQP （sequence of quadratic programming） method with the nonlinear complementarity problem （NCP） function is described for constrained nonlinear optimization problem.We introduce an NCP function into the filter and construct a new SQP-filter algorithm.Such methods are characterized by their use of the dominance concept of multi-objective optimization,instead of a penalty parameter whose adjustment can be problematic.We prove that the algorithm has global convergence and superlinear convergence rates under some mild conditions.

Smoothing Inexact Newton Method for Solving P_0-NCP Problems

Based on a smoothing symmetric disturbance FB-function,a smoothing inexact Newton method for solving the nonlinear complementarity problem with P0-function was proposed.It was proved that under mild conditions,the given algorithm performed global and superlinear convergence without strict complementarity.For the same linear complementarity problem(LCP),the algorithm needs similar iteration times to the literature.However,its accuracy is improved by at least 4 orders with calculation time reduced by almost 50%,and the iterative number is insensitive to the size of the LCP.Moreover,fewer iterations and shorter time are required for solving the problem by using inexact Newton methods for different initial points.

Regularization Semismooth Newton Method for P_0-NCPs with Non-monotone Line Search

Based on the generalized Fischer-Burmeister function, Chen et al in 2008 put forward a regularization semismooth Newton method for solving the nonlinear complementarity problem with a P0-function. In this paper, we investigate the above algorithm with the monotone line search replaced by a non-monotone line search. It is shown that the non-monotone algorithm is well-defined, and is globally and locally superlinearly convergent under standard assumptions.

蛋白质折叠、动力学以及蛋白质-配体结合的物理化学基础

蛋白质是生物体的重要组成部分并参与细胞内几乎所有的生物学过程.随着越来越多物种基因组序列的测定,准确理解基因产物的功能并探索蛋白质功能多样性的原因,已经成为当前的研究热点.为了研究蛋白质的功能,已有大量蛋白质的静态三维结构被测定.但是,蛋白功能最终受其动力学行为所控制,这包括折叠过程、构象波动、分子运动以及蛋白质-配体相互作用等.基于自由能图谱理论,本文深入讨论了蛋白质动力学的底层物理化学机制,并回答了以下问题:蛋白质为什么能够折叠、以及如何折叠成其天然三维结构?为什么蛋白质的动力学特征是固有的?其动力学行为如何控制蛋白质的功能?讨论结果将有助于后基因组时代生命科学研究中蛋白质结构-功能关系的理解.

A New Successive Approximation Damped Newton Method for Nonlinear Complementarity Problems

In this paper, we present a new successive approximation damped Newton method for the nonlinear complementarity problem based on its equivalent nonsmooth equations. Under suitable conditions, we obtain the global convergence result of the proposed algorithms. Some numerical results are also reported.

A complementary formulation for traffic equilibrium problem with a new nonadditive route cost

Improviag transportation system is essential for all people in each city since transport plays a very important role. Using mathematical programming approach transport problem is an effective way to improve transportation system. In this paper, the traffic equilibrium problem （TEP） with a general nonadditive route cost function is studied. We formulate the route cost function for each route as a disutility function, which can evaluate route cost function flexibly and analyze the route toll conveniently. Furthermore, we present the TEP with a nonlinear complementary problem （NCP） formulation. The monotonicity and the existence with the NCP formulation are also given under relative assumptions.

Condensed form of complementarity formulation for discontinuous deformation analysis

While the classical discontinuous deformation analysis(DDA) is applied to the analysis of a given block system, one must preset stiffness parameters for artificial springs to be fixed during the open-close iteration. To a great degree, success or failure in applying DDA to a practical problem is dependent on the spring stiffness parameters, which is believed to be the biggest obstacle to more extensive applications of DDA. In order to evade the introduction of the artificial springs, this study reformulates DDA as a mixed linear complementarity problem(MLCP) in the primal form. Then, from the fact that the block displacement vector of each block can be expressed in terms of the contact forces acting on the block, the condensed form of MLCP is derived, which is more efficient than the primal form. Some typical examples including those designed by the DDA inventor are reanalyzed, proving that the procedure is feasible.