Jamrog, Diane C.; Phillips, George N. jun.; Tapia, Richard A.; Zhang, Yin A global optimization method for the molecular replacement problem in X-ray crystallography. (English) Zbl 1120.82310 Math. Program. 103, No. 2 (B), 399-426 (2005). MSC: 82D25 90C90 92E10 PDFBibTeX XMLCite \textit{D. C. Jamrog} et al., Math. Program. 103, No. 2 (B), 399--426 (2005; Zbl 1120.82310) Full Text: DOI Link
Villalobos, M. C.; Tapia, R. A.; Zhang, Y. Sphere of convergence of Newton’s method on two equivalent systems from nonlinear programming. (English) Zbl 1076.90067 J. Optimization Theory Appl. 121, No. 3, 489-514 (2004). MSC: 90C53 65K05 90C51 PDFBibTeX XMLCite \textit{M. C. Villalobos} et al., J. Optim. Theory Appl. 121, No. 3, 489--514 (2004; Zbl 1076.90067) Full Text: DOI
Jamrog, D. C.; Tapia, R. A.; Zhang, Y. Comparison of two sets of first-order conditions as bases of interior-point Newton methods for optimization with simple bounds. (English) Zbl 1172.90502 J. Optim. Theory Appl. 113, No. 1, 21-40 (2002). Reviewer: Francisco Guerra Vazquez (Puebla) MSC: 90C46 90C26 68Q25 PDFBibTeX XMLCite \textit{D. C. Jamrog} et al., J. Optim. Theory Appl. 113, No. 1, 21--40 (2002; Zbl 1172.90502) Full Text: DOI
Villalobos, C.; Tapia, R.; Zhang, Y. Local behavior of the Newton method on two equivalent systems from linear programming. (English) Zbl 0990.90066 J. Optimization Theory Appl. 112, No. 2, 239-263 (2002). Reviewer: Rembert Reemtsen (Cottbus) MSC: 90C05 90C51 65K05 PDFBibTeX XMLCite \textit{C. Villalobos} et al., J. Optim. Theory Appl. 112, No. 2, 239--263 (2002; Zbl 0990.90066) Full Text: DOI
Wu, Zhijun; Phillips, George N. jun.; Tapia, Richard; Zhang, Yin A fast Newton algorithm for entropy maximization in phase determination. (English) Zbl 0992.65069 SIAM Rev. 43, No. 4, 623-642 (2001). Reviewer: Hans Benker (Merseburg) MSC: 65K05 65C60 65H10 62C10 90C25 90C30 90C34 92C05 92C40 92C55 PDFBibTeX XMLCite \textit{Z. Wu} et al., SIAM Rev. 43, No. 4, 623--642 (2001; Zbl 0992.65069) Full Text: DOI
Velázquez, L.; Phillips, G. N. jun.; Tapia, R. A.; Zhang, Y. Selective search for global optimization of zero or small residual least-squares problems: A numerical study. (English) Zbl 0990.90109 Comput. Optim. Appl. 20, No. 3, 299-315 (2001). MSC: 90C30 PDFBibTeX XMLCite \textit{L. Velázquez} et al., Comput. Optim. Appl. 20, No. 3, 299--315 (2001; Zbl 0990.90109) Full Text: DOI
Zhang, Y.; Tapia, R.; Velázquez, L. On convergence of minimization methods: Attraction, repulsion, and selection. (English) Zbl 0969.90084 J. Optimization Theory Appl. 107, No. 3, 529-546 (2000). MSC: 90C30 90C46 PDFBibTeX XMLCite \textit{Y. Zhang} et al., J. Optim. Theory Appl. 107, No. 3, 529--546 (2000; Zbl 0969.90084) Full Text: DOI
El-Bakry, A. S.; Tapia, R. A.; Zhang, Y. On the convergence rate of Newton interior-point methods in the absence of strict complementarity. (English) Zbl 0862.90120 Comput. Optim. Appl. 6, No. 2, 157-167 (1996). MSC: 90C33 PDFBibTeX XMLCite \textit{A. S. El-Bakry} et al., Comput. Optim. Appl. 6, No. 2, 157--167 (1996; Zbl 0862.90120) Full Text: DOI
El-Bakry, A. S.; Tapia, R. A.; Tsuchiya, T.; Zhang, Y. On the formulation and theory of the Newton interior-point method for nonlinear programming. (English) Zbl 0851.90115 J. Optimization Theory Appl. 89, No. 3, 507-541 (1996). MSC: 90C30 65K05 90C05 PDFBibTeX XMLCite \textit{A. S. El-Bakry} et al., J. Optim. Theory Appl. 89, No. 3, 507--541 (1996; Zbl 0851.90115) Full Text: DOI
Tapia, R.; Zhang, Y.; Saltzman, M.; Weiser, A. The Mehrotra predictor-corrector interior-point method as a perturbated composite Newton method. (English) Zbl 0846.65024 SIAM J. Optim. 6, No. 1, 47-56 (1996). Reviewer: H.Hollatz (Magdeburg) MSC: 65K05 90C05 PDFBibTeX XMLCite \textit{R. Tapia} et al., SIAM J. Optim. 6, No. 1, 47--56 (1996; Zbl 0846.65024) Full Text: DOI
Tapia, Richard A.; Zhang, Yin; Ye, Yinyu On the convergence of the iteration sequence in primal-dual interior- point methods. (English) Zbl 0834.90090 Math. Program. 68, No. 2 (A), 141-154 (1995). MSC: 90C05 PDFBibTeX XMLCite \textit{R. A. Tapia} et al., Math. Program. 68, No. 2 (A), 141--154 (1995; Zbl 0834.90090)
El-Bakry, A. S.; Tapia, R. A.; Zhang, Y. A study of indicators for identifying zero variables in interior-point methods. (English) Zbl 0801.65056 SIAM Rev. 36, No. 1, 45-72 (1994). Reviewer: J.Terno (Dresden) MSC: 65K05 90C05 PDFBibTeX XMLCite \textit{A. S. El-Bakry} et al., SIAM Rev. 36, No. 1, 45--72 (1994; Zbl 0801.65056) Full Text: DOI Link
Ye, Y.; Güler, O.; Tapia, R. A.; Zhang, Y. A quadratically convergent \(O(\sqrt n\;L)\)-iteration algorithm for linear programming. (English) Zbl 0778.90037 Math. Program. 59, No. 2 (A), 151-162 (1993). MSC: 90C05 90-08 90C60 PDFBibTeX XMLCite \textit{Y. Ye} et al., Math. Program. 59, No. 2 (A), 151--162 (1993; Zbl 0778.90037) Full Text: DOI
Zhang, Yin; Tapia, Richard; Potra, Florian On the superlinear convergence of interior-point algorithms for a general class of problems. (English) Zbl 0781.90074 SIAM J. Optim. 3, No. 2, 413-422 (1993). MSC: 90C20 90-08 90C33 65K05 90C05 PDFBibTeX XMLCite \textit{Y. Zhang} et al., SIAM J. Optim. 3, No. 2, 413--422 (1993; Zbl 0781.90074) Full Text: DOI Link
Zhang, Yin; Tapia, Richard A. A superlinearly convergent polynomial primal-dual interior-point algorithm for linear programming. (English) Zbl 0781.90067 SIAM J. Optim. 3, No. 1, 118-133 (1993). MSC: 90C05 90-08 65K05 PDFBibTeX XMLCite \textit{Y. Zhang} and \textit{R. A. Tapia}, SIAM J. Optim. 3, No. 1, 118--133 (1993; Zbl 0781.90067) Full Text: DOI Link
Zhang, Yin; Tapia, Richard A.; Dennis, John E. jun. On the superlinear and quadratic convergence of primal-dual interior point linear programming algorithms. (English) Zbl 0763.90066 SIAM J. Optim. 2, No. 2, 304-324 (1992). MSC: 90C05 90-08 PDFBibTeX XMLCite \textit{Y. Zhang} et al., SIAM J. Optim. 2, No. 2, 304--324 (1992; Zbl 0763.90066) Full Text: DOI Link
Byrd, R. H.; Tapia, R. A.; Zhang, Yin An SQP augmented Lagrangian BFGS algorithm for constrained optimization. (English) Zbl 0773.90065 SIAM J. Optim. 2, No. 2, 210-241 (1992). MSC: 90C30 90-08 65K05 49M37 PDFBibTeX XMLCite \textit{R. H. Byrd} et al., SIAM J. Optim. 2, No. 2, 210--241 (1992; Zbl 0773.90065) Full Text: DOI Link
Zhang, Y.; Tapia, R. A. Superlinear and quadratic convergence of primal-dual interior-point methods for linear programming revisited. (English) Zbl 0792.90078 J. Optimization Theory Appl. 73, No. 2, 229-242 (1992). MSC: 90C30 PDFBibTeX XMLCite \textit{Y. Zhang} and \textit{R. A. Tapia}, J. Optim. Theory Appl. 73, No. 2, 229--242 (1992; Zbl 0792.90078) Full Text: DOI
Tapia, R. A.; Zhang, Yin An optimal-basis identification technique for interior-point linear programming algorithms. (English) Zbl 0737.65052 Linear Algebra Appl. 152, 343-363 (1991). Reviewer: Xu Chengxian (Xian) MSC: 65K05 90C05 PDFBibTeX XMLCite \textit{R. A. Tapia} and \textit{Y. Zhang}, Linear Algebra Appl. 152, 343--363 (1991; Zbl 0737.65052) Full Text: DOI
Tapia, R. A.; Zhang, Y. Cubically convergent method for locating a nearby vertex in linear programming. (English) Zbl 0696.90036 J. Optimization Theory Appl. 67, No. 2, 217-225 (1990). Reviewer: R.A.Tapia MSC: 90C05 65K05 90-08 PDFBibTeX XMLCite \textit{R. A. Tapia} and \textit{Y. Zhang}, J. Optim. Theory Appl. 67, No. 2, 217--225 (1990; Zbl 0696.90036) Full Text: DOI