SQP, an abbreviation for Sequential Quadratic Programming, is a mathematical optimization technique used to solve constrained optimization problems. It is a modified version of the quadratic programming (QP) method, which is particularly useful when dealing with non-linear objective functions and constraints.
SQP works by iteratively solving a sequence of QP subproblems, each of which is a quadratic programming problem. At each iteration, SQP uses the solution of the previous QP subproblem to determine the next search direction. This process continues until convergence is reached or a specified stopping criterion is met.
The main advantage of SQP is its ability to handle both equality and inequality constraints simultaneously, making it suitable for a wide range of practical applications. By incorporating these constraints into a sequence of QP subproblems, SQP allows for the efficient and accurate solution of non-linear optimization problems in engineering, finance, operations research, and other fields.
Furthermore, SQP algorithms can also take advantage of problem-specific structure or exploit problem-specific information to improve their efficiency. This makes them highly flexible and adaptable to various problem domains.
In summary, SQP is a powerful optimization technique used for solving non-linear constrained optimization problems. It combines quadratic programming subproblems with iterative refinement to find optimal solutions efficiently. Its versatility and ability to handle both equality and inequality constraints make it a valuable tool in various industries and research fields.
