The Full Form of SQP is‍ Sequential quadratic programming.

Sequential quadratic programming (SQP) is one of the most effective methods for nonlinearly constrained optimization problems. The method generates steps by solving quadratic subproblems; it can be used both in line search and trust-region frameworks. SQP is appropriate for small and large problems and it is well-suited to solving problems with significant nonlinearities.

The SQP method can be viewed as a generalization of Newton’s method for unconstrained optimization in that it finds a step away from the current point by minimizing a quadratic model of the problem. A number of software packages (NPSOL, NLPQL, OPSYC, OPTIMA, MATLAB, and SQP) are based on this approach. In its purest form, the SQP algorithm replaces the objective function with the quadratic approximation

qk(d)=∇f(xk)Td+12dT∇2xxL(xk,λk)d