sequential convex programming

Sequential convex programming (SCP) is a numerical optimization method used to solve non-convex optimization problems by iteratively solving a sequence of convex subproblems. The approach is based on the concept of transforming a non-convex problem into a series of convex subproblems that are easier to solve.

In SCP, the original non-convex problem is divided into a sequence of convex subproblems, which are solved in a sequential manner. At each iteration, the solution obtained from the previous subproblem is used as a starting point for the current subproblem. The solution obtained from the current subproblem is then used as a starting point for the next subproblem.

SCP is particularly useful in solving optimization problems where the objective function is non-convex, but the constraints are convex. The method is commonly used in engineering, economics, and finance, as well as in machine learning and data science applications.

One of the advantages of SCP is that it converges to a locally optimal solution in a finite number of iterations. However, SCP does not guarantee convergence to a global optimum, and the quality of the solution obtained depends on the quality of the starting point and the convex approximations used in each subproblem.