SEQUENTIAL QUADRATIC PROGRAMMING Meaning and
Definition
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Sequential quadratic programming (SQP) is an optimization algorithm used to solve nonlinear programming problems. It is a mathematical technique that aims to find the optimal solution for a given problem by iteratively refining a set of feasible solutions. The key feature of SQP is its ability to handle both equality and inequality constraints.
In SQP, the problem is first formulated as a mathematical model with a set of objective and constraint functions. These functions involve a set of variables that need to be optimized. The algorithm then seeks to minimize the objective function while satisfying the constraints by iteratively adjusting the values of the variables.
The optimization process in SQP involves solving a sequence of quadratic programming subproblems. At each iteration, a quadratic approximation of the objective and constraint functions is made based on the current set of variables. This approximation is then solved to obtain the next set of variables, ensuring that the constraints are satisfied.
This method continues until convergence is achieved, meaning the algorithm reaches an optimal solution within the specified tolerances. SQP is known for its efficiency and effectiveness in finding globally optimal solutions for a wide range of nonlinear programming problems. It is often utilized in various fields such as engineering, economics, and finance, where the optimization of complex systems and processes is required.
