<p>&lt;p&gt;Convex optimization is a branch of applied mathematics, which has been well-established in recent years and has played a major role in solving a large number of scientific and engineering problems. Typical optimization schemes, such as least squares and linear programming, are special cases of convex optimization. By relying on the convex optimization theory, many problems that were previously unsolvable or difficult to implement in engineering have been successfully solved. This course focuses on introducing the basic principles of convex optimization and its applications in signal processing. We will focus on teaching the concepts and definitions of convex sets, convex functions, convex optimization problems, Lagrange duality theory, linear programming, second-order cone programming, quadratic programming, positive semi-definite programming, geometric programming and other optimization problems, as well as typical algorithms such as gradient descent, Newton's method and interior point method. On this basis, we will teach the application of convex optimization in typical signal processing problems, including filter design, parameter estimation, pattern recognition, machine learning, and statistical inference. Through the study of this course, students will be able to master the basic principles of convex optimization, understand how abstract mathematical theories can be applied to practical engineering problems, as well as the design and implementation principles of typical optimization algorithms.&lt;/p&gt;</p>