No abstract

No abstract

Abstract. This paper considers the optimization problem of minimizing a rational function. We reformulate this problem as polynomial optimization by the technique of homogenization. These two problems are shown to be equivalent under some generic conditions. The exact Jacobian SDP relaxation method proposed by Nie is used to solve the resulting polynomial optimization. We also prove that the assumption of nonsingularity in Nie's method can be weakened as the finiteness of singularities. Some numerical examples are given to illustrate the efficiency of our method.

No abstract

This paper studies the saddle point problem of polynomials. We give an algorithm for computing saddle points. It is based on solving Lasserre’s hierarchy of semidefinite relaxations. Under some genericity assumptions on defining polynomials, we show that: (i) if there exists a saddle point, our algorithm can get one by solving a finite hierarchy of Lasserre-type semidefinite relaxations; (ii) if there is no saddle point, our algorithm can detect its nonexistence.

P-tensor and P 0 -tensor are introduced in tensor complementarity problem, which have wide applications in game theory. In this paper, we establish SDP relaxation algorithms for detecting P(P 0 )-tensor. We first reformulate P(P 0 )-tensor detection problem as polynomial optimization problems. Then we propose the SDP relaxation algorithms for solving the reformulated polynomial optimization problems. Numerical examples are reported to show the efficiency of the proposed algorithms.

For electrified transportation (eTransportation) systems, multi-phase motors can provide higher performance and reliability than three-phase ones, but also bring more challenges in their optimal design and control. In this article, a set of high reliable electric drive system based on dual three-phase permanent magnet synchronous motor (DTP PMSM) is developed for auxiliary systems in eTransportation field. A digital collaborative develop process is proposed with the support of multiple software tools. Design, manufacture, and bench testing stages of the DTP PMSM, the two-level six-phase inverter, and the control algorithm are efficiently incorporated. A prototype of the multi-phase electric drive system is fabricated and tested. Comparison of the simulation analysis and experimental results confirms the effectiveness of the collaborative develop progress. Control algorithms based on dual d-q model and vector space decomposition model are both verified and compared via the bench test. Operation mode switching from six-phase mode to three-phase mode is also realized with the prototype system, verifying its capability in fault-tolerant and potential in efficiency optimizing. INDEX TERMS Dual three-phase motor, auxiliary electric drive system, transportation electrification, digital collaborative development, motor design and control.

This paper studies the saddle point problem of polynomials. We give an algorithm for computing saddle points. It is based on solving Lasserre's hierarchy of semidefinite relaxations. Under some genericity assumptions on defining polynomials, we show that: i) if there exists a saddle point, our algorithm can get one by solving a finite number of Lasserre type semidefinite relaxations; ii) if there is no saddle point, our algorithm can detect its nonexistence.