A trust region SQP-filter method for nonlinear second-order cone programming

A trust region SQP algorithm for mixed-integer nonlinear programming

We propose a modified sequential quadratic programming (SQP) method for solving mixed-integer nonlinear programming problems. Under the assumption that integer variables have a smooth influence on the model functions, i.e., that function values do not change drastically when inor decrementing an integer value, successive quadratic approximations are applied. The algorithm is stabilized by a tru...

Sl1QP Based Algorithm with Trust Region Technique for Solving Nonlinear Second-Order Cone Programming Problems

In this paper, we propose an algorithm based on Fletcher’s Sl1QP method and the trust region technique for solving Nonlinear Second-Order Cone Programming (NSOCP) problems. The Sl1QP method was originally developed for nonlinear optimization problems with inequality constraints. It converts a constrained optimization problem into an unconstrained problem by using the l1 exact penalty function, ...

An SQP-type algorithm for nonlinear second-order cone programs

We propose an SQP-type algorithm for solving nonlinear second-order cone programming (NSOCP) problems. At every iteration, the algorithm solves a convex SOCP subproblem in which the constraints involve linear approximations of the constraint functions in the original problem and the objective function is a convex quadratic function. Those subproblems can be transformed into linear SOCP problems...

Global Convergence of a Trust-Region SQP-Filter Algorithm for General Nonlinear Programming

A trust-region SQP-filter algorithm of the type introduced by Fletcher and Leyffer [Math. Program., 91 (2002), pp. 239–269] that decomposes the step into its normal and tangential components allows for an approximate solution of the quadratic subproblem and incorporates the safeguarding tests described in Fletcher, Leyffer, and Toint [On the Global Convergence of an SLPFilter Algorithm, Technic...

Global Convergence of a Hybrid Trust-Region SQP-Filter Algorithm for General Nonlinear Programming