Particle swarm optimization algorithm based on parametric equation method to handle equality constraints;

The Descending Dimension Algorithm by a Nonlinear System of Equations of the Programming Problems with Equality Constraints;

In the paper, equality constraints after networks distributed are included into objective function with Lagrange multiplier based on PMUs, so the problem of the distributed state estimation is changed into optimization problem with equality constraints, realized the distributed paral.

In such a method,the strongly coupled connected components are broken by introducing equivalent constraints and tearing part of the constraints,and a solving sequence which only includes basic geometric elements is obtained.

Implying a multivariate equality constraint in switching function, a genetic algorithm (GA) based improved mathematical model for fault location of distribution network is built.

For a class of networked control systems(NCS) with equality constraint,this paper addresses the problem of designing controller,sampling period and the maximum allowable delay bound(MADB).

A multivariable equality constraint condition is hidden in switching functions through different equivalent transformations.

Based on unified strength theory solution of thickness cylinder,according to the characteristics and equivalent restriction reduction factor of concrete,circle hollow section(CHS) inner and square hollow section(SHS) outer concrete-filled double skin tubes were equivalent to CHS inner and CHS outer concrete-filled double skin tubes through introducing concrete strength reduction factor.