A Sequential Quadratically Constrained Quadratic Programming Method for Differentiable Convex Minimization

Authors:
Masao Fukushima;Zhi-Quan Luo;Paul Tseng
Affiliations:
-;-;-
Venue:
SIAM Journal on Optimization
Year:
2002

Citing 0
Cited 7

On local convergence of sequential quadratically-constrained quadratic-programming type methods, with an extension to variational problems

Computational Optimization and Applications
A sequential quadratically constrained quadratic programming method with an augmented Lagrangian line search function

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A Truncated SQP Method Based on Inexact Interior-Point Solutions of Subproblems

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A working set SQCQP algorithm with simple nonmonotone penalty parameters

Journal of Computational and Applied Mathematics
An Optimal Algorithm for Minimization of Quadratic Functions with Bounded Spectrum Subject to Separable Convex Inequality and Linear Equality Constraints

SIAM Journal on Optimization
Sharp Primal Superlinear Convergence Results for Some Newtonian Methods for Constrained Optimization

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A superlinearly convergent SQP method without boundedness assumptions on any of the iterative sequences

Journal of Computational and Applied Mathematics

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Abstract

This paper presents a sequential quadratically constrained quadratic programming (SQCQP) method for solving smooth convex programs. The SQCQP method solves at each iteration a subproblem that involves convex quadratic inequality constraints as well as a convex quadratic objective function. Such a quadratically constrained quadratic programming problem can be formulated as a second-order cone program, which can be solved efficiently by using interior point methods. We consider the following three fundamental issues on the SQCQP method: the feasibility of subproblems, the global convergence, and the quadratic rate of convergence. In particular, we show that the Maratos effect is avoided without any modification to the search direction, even though we use an ordinary $\ell_1$ exact penalty function as the line search merit function.