sequential convex programming

Sequential convex programming (SCP) is a method used in optimization to solve non-convex problems by iteratively solving a sequence of convex subproblems. The basic idea is to approximate the original non-convex problem with a sequence of simpler convex problems, and then solve each of these subproblems to obtain a sequence of candidate solutions.

The algorithm starts with an initial guess for the solution, and then iteratively updates this guess by solving a convex subproblem at each step. The objective function and constraints of the original problem are replaced with a convex approximation, usually using a linearization or quadratic approximation. The resulting convex subproblem is then solved using a variety of optimization techniques, such as gradient descent or interior point methods.

After each convex subproblem is solved, the algorithm updates the solution by moving towards the new point that minimizes the approximation error. This process continues until the solution converges to a stationary point of the original non-convex problem.

SCP has been successfully applied to a wide range of optimization problems, including machine learning, control, and finance. It is a powerful tool for solving non-convex problems that cannot be handled by traditional optimization methods.