In the context of new engineering, the cultivation of scientific and technological talents should fully consider new technical qualities such as service to the country, innovation and progress, formation of environmental awareness, and formation of international vision. With the rapid development and progress of socialist market economy, the scope of application of scientific and technological revolution has been gradually expanded. The application of mechanical engineering is getting wider and wider. Under the background of new engineering education, in mechanical engineering, many linear programming models can be transformed into standard models using some mathematical methods, which can be used to solve them. In mechanical engineering, there exist not only linear optimization problems with continuous variables, but also linear optimization problems with all or some variables as a set of deterministic values. Linear optimization problems in mechanical engineering often manifest themselves as mixed discrete optimization due to constraints of standardization, serialization, standardization, design, assembly and verification, and objective requirements. This thesis introduces the KarmarKar improvement algorithm and extends the application of the KarmarKar improvement algorithm in mechanical engineering with the example of hybrid linear optimization in mechanical engineering.