P-order Cone Complementarity Problem And The Study Of Properties Of The Quantum Behaved Particle Swarm Optimization

P-order cone complementarity problem(PCP) is a natural extension of the second-order cone complementarity problem(SCCP). Since p-order cone programming has new theories, rich contents and wide applications, it has turned into part of the significant search directions in optimization fields in recent decades; As a new extension of the particle swarm optimization(PSO) method, the quantum behave particle swarm optimization(QPSO) method also belongs to a kind of evolutionary methods, Since QPSO method has a lot of good advantages, including globally convergence, good stability and fast convergence rate which were hardly existence for most other evolutionary optimization techniques, it has become one of the significant research directions in evolutionary algorithm fields in recent years, Both of the above-mentioned directions have been researched greatly by majority of scholars and experts. This paper is greatly focuses on establishing derivative-free descent methods to solve the PCP and studying the properties of the QPSO method. The main results achieves in this thesis are summarized as follows:In this thesis, we consider the PCP in a Hilbert space. For solving the PCP, we establish a new derivative-free descent algorithm in view of several favorable properties of the implicit Lagrangian merit function which was proposed by Lu and Huang. Moreover, we prove that this new method is globally convergent with some appropriate assumptions and settings.In this thesis, we test QPSO method and w particle swarm optimization(w PSO) algorithm respectively on three unimodal benchmark functions and three multimodal benchmark functions to find their global optimal values. The experimental consequences show that the former algorithm has many advantages in good stability and globally convergent and so on. Furthermore, we conclude two new properties of QPSO method which are not correct for w PSO algorithm.