This paper addresses the challenge of multi-objective optimization, where multiple conflicting objectives often need to be optimized simultaneously. Traditional methods, such as linear scalarization and classical Tchebycheff scalarization, have limitations in terms of computational complexity and theoretical properties. To overcome these issues, the authors propose a smooth Tchebycheff (STCH) scalarization approach, which leverages smooth optimization techniques to achieve faster convergence and lower computational complexity while maintaining good theoretical properties. The STCH scalarization is designed for gradient-based multi-objective optimization and is shown to have several advantages over existing methods. It can find all Pareto solutions under mild conditions, with a faster convergence rate compared to the classical Tchebycheff scalarization. The authors provide detailed theoretical analyses to support the effectiveness of the STCH scalarization, including its ability to find all Pareto solutions and its convergence guarantees. Experimental results on various real-world applications, such as multi-task learning and engineering design problems, demonstrate the effectiveness and efficiency of the STCH scalarization. The method outperforms or matches the performance of other methods, including adaptive gradient algorithms, while offering a simpler and more efficient approach. The paper also discusses the potential for using the STCH scalarization in Pareto set learning, showing that it can improve the quality of Pareto front approximations. Overall, the STCH scalarization is presented as a lightweight and efficient method for gradient-based multi-objective optimization, with promising theoretical and practical implications.This paper addresses the challenge of multi-objective optimization, where multiple conflicting objectives often need to be optimized simultaneously. Traditional methods, such as linear scalarization and classical Tchebycheff scalarization, have limitations in terms of computational complexity and theoretical properties. To overcome these issues, the authors propose a smooth Tchebycheff (STCH) scalarization approach, which leverages smooth optimization techniques to achieve faster convergence and lower computational complexity while maintaining good theoretical properties. The STCH scalarization is designed for gradient-based multi-objective optimization and is shown to have several advantages over existing methods. It can find all Pareto solutions under mild conditions, with a faster convergence rate compared to the classical Tchebycheff scalarization. The authors provide detailed theoretical analyses to support the effectiveness of the STCH scalarization, including its ability to find all Pareto solutions and its convergence guarantees. Experimental results on various real-world applications, such as multi-task learning and engineering design problems, demonstrate the effectiveness and efficiency of the STCH scalarization. The method outperforms or matches the performance of other methods, including adaptive gradient algorithms, while offering a simpler and more efficient approach. The paper also discusses the potential for using the STCH scalarization in Pareto set learning, showing that it can improve the quality of Pareto front approximations. Overall, the STCH scalarization is presented as a lightweight and efficient method for gradient-based multi-objective optimization, with promising theoretical and practical implications.