A Linearly Convergent Dual-Based Gradient Projection Algorithm for Quadratically Constrained Convex Minimization

References

• Auslender A., Teboulle M. Interior gradient and epsilon subgradient descent methods for constrained convex minimization. Math. Oper. Res. (2004) 29:1–26Link, Google Scholar
• Beck A., Teboulle M. Mirror descent and nonlinear projected subgradient methods for convex optimization. Oper. Res. Lett. (2003) 31:167–175Crossref, Google Scholar
• Ben-Tal A., Margalit T., Nemirovski A. The ordered subsets mirror descent optimization method with applications to tomography. SIAM J. Optim. (2001) 12:79–108Crossref, Google Scholar
• Bertsekas D. On the Goldstein-Levitin-Polyak gradient projection method. IEEE Trans. Automatic Control (1976) 21:174–184Crossref, Google Scholar
• Bertsekas D.Nonlinear Programming (1999) 2nd ed.(Athena Scientific, Belmont, MA) Google Scholar
• Bertsekas D., Tsitsiklis J.Parallel Distributed Computation: Numerical Methods (1997) (Athena Scientific, Belmont, MA) Google Scholar
• Bienstock D.Potential Function Methods for Approximately Solving Linear Programming Problems: Theory and Practice. International Series in Operations Research and Management Science (2002) 53(Kluwer Academic Publishers, Boston, MA) Google Scholar
• Burke J. V., Moré J. J. On the identification of active constraints. SIAM J. Numer. Anal. (1988) 25:1197–1211Crossref, Google Scholar
• Calamai P. H., Moré J. J. Projected gradient methods for linearly constrained problems. Math. Programming (1987) 39:98–116Crossref, Google Scholar
• Dunn J. C. Global and asymptotic convergence rate estimates for a class of projected gradient processes. SIAM J. Control Optim. (1981) 19:368–400Crossref, Google Scholar
• Dunn J. C. On the convergence of projected gradient processes to singular critical points. J. Optim. Theory Appl. (1987) 55:203–216Crossref, Google Scholar
• Goldstein A. A. Convex programming in Hilbert space. Bull. Amer. Math. Soc. (1964) 70:709–710Crossref, Google Scholar
• Levitin E. S., Polyak B. T. Constrained minimization methods. USSR Comput. Math. Math. Phys. (1966) 6:787–823Crossref, Google Scholar
• Lin A., Han S. P. A class of methods for projection on the intersection of several ellipsoids. SIAM J. Optim. (2004) 15:129–138Crossref, Google Scholar
• Luo Z. Q. New error bounds and their applications to convergence analysis of iterative algorithms. Math. Programming (2000) 88:341–355Crossref, Google Scholar
• Luo Z. Q., Tseng P. Error bound and the convergence analysis of matrix splitting algorithms for the affine variational inequality problem. SIAM J. Optim. (1992a) 2:43–54Crossref, Google Scholar
• Luo Z. Q., Tseng P. On the linear convergence of descent methods for convex essentially smooth minimization. SIAM J. Control Optim. (1992b) 30:408–425Crossref, Google Scholar
• Luo Z. Q., Tseng P. On the convergence rate of dual ascent methods for linearly constrained convex minimization. Math. Oper. Res. (1993a) 18:846–867Link, Google Scholar
• Luo Z. Q., Tseng P. Error bounds and convergence analysis of feasible descent methods: A general approach. Ann. Oper. Res. (1993b) 46:157–178Crossref, Google Scholar
• Nemirovski A. Prox-method with rate of convergence O(1/t) for variational inequalities with Lipschitz continuous monotone operators and smooth convex-concave saddle point problems. SIAM J. Optim. (2004) 15:229–251Crossref, Google Scholar
• Nemirovski A., Yudin D.Problem Complexity and Method Efficiency in Optimization (1983) (John Wiley, New York, NY) Google Scholar
• Nesterov Y., Nemirovski A.Interior Point Polynomial Algorithms in Convex Programming (1994) (SIAM Publications, Philadelphia, PA) Crossref, Google Scholar
• Pang J. S. Error bounds in mathematical programming. Math. Programming (1997) 79:299–332Crossref, Google Scholar
• Polyak B. T.Introduction to Optimization (1987) (Optimization Software Inc., New York) Google Scholar
• Rockafellar R. T.Convex Analysis (1970) (Princeton University Press, Princeton, NJ) Crossref, Google Scholar
• Rockafellar R. T. Monotone operators and the proximal point algorithm. SIAM J. Control Optim. (1976) 14:877–898Crossref, Google Scholar
• Wang C., Xiu N. Convergence of the gradient projection method for generalized convex minimization. Comput. Optim. Appl. (2000) 16:111–120Crossref, Google Scholar