메뉴 건너뛰기




Volumn 34, Issue 1, 2009, Pages 124-141

Local duality of nonlinear semidefinite programming

Author keywords

Constraint nondegeneracy; Nonlinear semidefinite programming; Nonsingularity; Strong second order sufficient condition

Indexed keywords

CONSTRAINT NONDEGENERACY; CORRELATION MATRIX; KARUSH KUHN TUCKERS; LAGRANGIAN FUNCTIONS; NON-DEGENERACY; NONLINEAR PROGRAMS; NONLINEAR SEMIDEFINITE PROGRAMMING; NONSINGULARITY; POSITIVE DEFINITE; SECOND-ORDER SUFFICIENT CONDITIONS; SEMI-DEFINITE PROGRAMMING; STABILITY ANALYSIS; STRONG SECOND-ORDER SUFFICIENT CONDITION;

EID: 67649960105     PISSN: 0364765X     EISSN: 15265471     Source Type: Journal    
DOI: 10.1287/moor.1080.0315     Document Type: Article
Times cited : (22)

References (35)
  • 1
    • 0031141136 scopus 로고    scopus 로고
    • Complementarity and nondegeneracy in semidefinite programming
    • Alizadeh, F., J.-P. A. Haeberly, M. L. Overton. 1997. Complementarity and nondegeneracy in semidefinite programming. Math. Programming 77 111-128.
    • (1997) Math. Programming , vol.77 , pp. 111-128
    • Alizadeh, F.1    Haeberly, J.-P.A.2    Overton, M.L.3
  • 2
    • 84927914894 scopus 로고
    • On matrices depending on parameters
    • Arnold, V. I. 1971. On matrices depending on parameters. Russian Math. Surveys 26 29-43.
    • (1971) Russian Math. Surveys , vol.26 , pp. 29-43
    • Arnold, V.I.1
  • 3
    • 27244440823 scopus 로고    scopus 로고
    • Strong regularity of semidefinite programming problems
    • Department of Mathematical Engineering, Universida de Chile
    • Bonnans, J. F., H. Ramírez C. 2005. Strong regularity of semidefinite programming problems. Techical report, Department of Mathematical Engineering, Universida de Chile.
    • (2005) Techical report
    • Bonnans, J.F.H.1    Ramírez, C.2
  • 4
    • 0032354477 scopus 로고    scopus 로고
    • Nondegeneracy and quantitative stability of parameterized optimization problems with multiple solutions
    • Bonnans, J. F., A. Shapiro. 1998. Nondegeneracy and quantitative stability of parameterized optimization problems with multiple solutions. SIAM J. Optim. 8 940-946.
    • (1998) SIAM J. Optim , vol.8 , pp. 940-946
    • Bonnans, J.F.1    Shapiro, A.2
  • 6
    • 0032208079 scopus 로고    scopus 로고
    • Sensitivity analysis of optimization problems under second order regularity constraints
    • Bonnans, J. F., R. Cominetti, A. Shapiro. 1998. Sensitivity analysis of optimization problems under second order regularity constraints. Math. Oper. Res. 23 803-832.
    • (1998) Math. Oper. Res , vol.23 , pp. 803-832
    • Bonnans, J.F.1    Cominetti, R.2    Shapiro, A.3
  • 7
    • 0033434223 scopus 로고    scopus 로고
    • Second order optimality conditions based on parabolic second order tangent sets
    • Bonnans, J. F., R. Cominetti, A. Shapiro. 1999. Second order optimality conditions based on parabolic second order tangent sets. SIAM J. Optim. 9 466-493.
    • (1999) SIAM J. Optim , vol.9 , pp. 466-493
    • Bonnans, J.F.1    Cominetti, R.2    Shapiro, A.3
  • 8
    • 58049197110 scopus 로고    scopus 로고
    • Constraint nondegeneracy, strong regularity and nonsingularity in semidefinite programming
    • Chan, Z. X., D. Sun. 2008. Constraint nondegeneracy, strong regularity and nonsingularity in semidefinite programming. SIAM J. Optim. 19 370-396.
    • (2008) SIAM J. Optim , vol.19 , pp. 370-396
    • Chan, Z.X.1    Sun, D.2
  • 10
    • 0001303990 scopus 로고
    • Metric regularity, tangent sets and second order optimality conditions
    • Cominetti, R. 1990. Metric regularity, tangent sets and second order optimality conditions. J. Appl. Math. Optim. 21 265-287.
    • (1990) J. Appl. Math. Optim , vol.21 , pp. 265-287
    • Cominetti, R.1
  • 11
    • 0001918140 scopus 로고
    • On the basic theorem for complemenarity
    • Eaves, B. C. 1971. On the basic theorem for complemenarity. Math. Programming 1 68-75.
    • (1971) Math. Programming , vol.1 , pp. 68-75
    • Eaves, B.C.1
  • 12
    • 36148941392 scopus 로고    scopus 로고
    • Equivalence of two nondegeneracy conditions for semidefinite programs
    • Flegel, M. L., C. Kanzow. 2007. Equivalence of two nondegeneracy conditions for semidefinite programs. J. Optim. Theory Appl. 135 381-397.
    • (2007) J. Optim. Theory Appl , vol.135 , pp. 381-397
    • Flegel, M.L.1    Kanzow, C.2
  • 14
    • 0344153904 scopus 로고    scopus 로고
    • Computing the nearest correlation matrix - A problem from finance
    • Higham, N. J. 2002. Computing the nearest correlation matrix - A problem from finance. IMA J. Numer. Anal. 22 329-343.
    • (2002) IMA J. Numer. Anal , vol.22 , pp. 329-343
    • Higham, N.J.1
  • 15
    • 0037289395 scopus 로고    scopus 로고
    • Semidefinite programs: New search directions, smoothing-type methods, and numerical results
    • Kanzow, C., C. Nagel. 2002. Semidefinite programs: New search directions, smoothing-type methods, and numerical results. SIAM J. Optim. 13 1-23.
    • (2002) SIAM J. Optim , vol.13 , pp. 1-23
    • Kanzow, C.1    Nagel, C.2
  • 16
    • 0024011499 scopus 로고
    • An envelope-like effect of infinitely many inequality constraints on second order necessary conditions for minimization problems
    • Kawasaki, H. 1988. An envelope-like effect of infinitely many inequality constraints on second order necessary conditions for minimization problems. Math. Programming 41 73-96.
    • (1988) Math. Programming , vol.41 , pp. 73-96
    • Kawasaki, H.1
  • 18
    • 33646744638 scopus 로고    scopus 로고
    • An algebraic condition equivalent to strong stability of stationary solutions of nonlinear positive semidefinite programms
    • Matsumoto, T. 2005. An algebraic condition equivalent to strong stability of stationary solutions of nonlinear positive semidefinite programms. SIAM J. Optim. 16 452-470.
    • (2005) SIAM J. Optim , vol.16 , pp. 452-470
    • Matsumoto, T.1
  • 19
    • 0035729262 scopus 로고    scopus 로고
    • A predictor-corrector algorithm for QSDP combining Dikin-type and Newton centering steps
    • Nie, J. W., Y. X. Yuan. 2001. A predictor-corrector algorithm for QSDP combining Dikin-type and Newton centering steps. Ann. Oper. Res. 103 115-133.
    • (2001) Ann. Oper. Res , vol.103 , pp. 115-133
    • Nie, J.W.1    Yuan, Y.X.2
  • 20
    • 0038300039 scopus 로고    scopus 로고
    • Semismooth homeomorphisms and strong stability of semidefinite and Lorentz complementarity problems
    • Pang, J.-S., D. Sun, J. Sun. 2003. Semismooth homeomorphisms and strong stability of semidefinite and Lorentz complementarity problems. Math. Oper. Res. 28 39-63.
    • (2003) Math. Oper. Res , vol.28 , pp. 39-63
    • Pang, J.-S.1    Sun, D.2    Sun, J.3
  • 21
    • 0000607524 scopus 로고
    • Convergence analysis of some algorithms for solving nonsmooth equations
    • Qi, L. 1993. Convergence analysis of some algorithms for solving nonsmooth equations. Math. Oper. Res. 18 227-244.
    • (1993) Math. Oper. Res , vol.18 , pp. 227-244
    • Qi, L.1
  • 22
    • 0016962866 scopus 로고
    • First order conditions for general nonlinear optimization
    • Robinson, S. M. 1976. First order conditions for general nonlinear optimization. SIAM J. Appl. Math. 30 597-607.
    • (1976) SIAM J. Appl. Math , vol.30 , pp. 597-607
    • Robinson, S.M.1
  • 23
    • 0018977011 scopus 로고
    • Strongly regular generalized equations
    • Robinson, S. M. 1980. Strongly regular generalized equations. Math. Oper. Res. 5 43-62.
    • (1980) Math. Oper. Res , vol.5 , pp. 43-62
    • Robinson, S.M.1
  • 24
    • 0020901152 scopus 로고
    • Local structure of feasible sets in nonlinear programming, Part II: Nondegeneracy
    • Robinson, S. M. 1984. Local structure of feasible sets in nonlinear programming, Part II: Nondegeneracy. Math. Programming Stud. 22 217-230.
    • (1984) Math. Programming Stud , vol.22 , pp. 217-230
    • Robinson, S.M.1
  • 25
    • 0038047997 scopus 로고    scopus 로고
    • Constriant nondegeneracy in variational analysis
    • Robinson, S. M. 2003. Constriant nondegeneracy in variational analysis. Math. Oper. Res. 28 201-232.
    • (2003) Math. Oper. Res , vol.28 , pp. 201-232
    • Robinson, S.M.1
  • 27
    • 0031139858 scopus 로고    scopus 로고
    • First and second order analysis of nonlinear semidefinite programms
    • Shapiro, A. 1997. First and second order analysis of nonlinear semidefinite programms. Math. Programming 77 301-320.
    • (1997) Math. Programming , vol.77 , pp. 301-320
    • Shapiro, A.1
  • 28
    • 0242627080 scopus 로고    scopus 로고
    • Duality, optimality conditions and perturbation analysis
    • R. Saigal, L. Vandenberghe, H. Wolkowicz, eds, Kluwer Academic Publishers, Boston
    • Shapiro, A. 2000. Duality, optimality conditions and perturbation analysis. R. Saigal, L. Vandenberghe, H. Wolkowicz, eds. Semidefinite Programming and Applications Handbook. Kluwer Academic Publishers, Boston, 67-92.
    • (2000) Semidefinite Programming and Applications Handbook , pp. 67-92
    • Shapiro, A.1
  • 29
    • 4844226011 scopus 로고    scopus 로고
    • Sensitivity anlaysis of generalized equations
    • Shapiro, A. 2003. Sensitivity anlaysis of generalized equations. J. Math. Sci. 115 2554-2565.
    • (2003) J. Math. Sci , vol.115 , pp. 2554-2565
    • Shapiro, A.1
  • 30
    • 0000496360 scopus 로고
    • On eigenvalue optimization
    • Shapiro, A., M. K. H. Fan. 1995. On eigenvalue optimization. SIAM J. Optim. 5 552-569.
    • (1995) SIAM J. Optim , vol.5 , pp. 552-569
    • Shapiro, A.1    Fan, M.K.H.2
  • 31
    • 33746089809 scopus 로고    scopus 로고
    • The strong second-order sufficient condition and constraint nondegeneracy in nonlinear semidefinite programming and their implications
    • Sun, D. 2006. The strong second-order sufficient condition and constraint nondegeneracy in nonlinear semidefinite programming and their implications. Math. Oper. Res. 31 761-776.
    • (2006) Math. Oper. Res , vol.31 , pp. 761-776
    • Sun, D.1
  • 32
    • 0036474487 scopus 로고    scopus 로고
    • Semismooth matrix valued functions
    • Sun, D., J. Sun. 2002. Semismooth matrix valued functions. Math. Oper. Res. 27 150-169.
    • (2002) Math. Oper. Res , vol.27 , pp. 150-169
    • Sun, D.1    Sun, J.2
  • 33
    • 34547439695 scopus 로고    scopus 로고
    • An inexact primal-dual path-following algorithm for convex quadratic SDP
    • Toh, K. C. 2008. An inexact primal-dual path-following algorithm for convex quadratic SDP. Math. Programming 112 221-254.
    • (2008) Math. Programming , vol.112 , pp. 221-254
    • Toh, K.C.1
  • 34
    • 67649960686 scopus 로고    scopus 로고
    • Toh, K. C., R. H. Tütüncü, M. J. Todd. 2007. Inexact primal-dual path-following algorithms for a special class of convex quadratic SDP and related problems. Pacific J. Optim. 3 135-164.
    • Toh, K. C., R. H. Tütüncü, M. J. Todd. 2007. Inexact primal-dual path-following algorithms for a special class of convex quadratic SDP and related problems. Pacific J. Optim. 3 135-164.
  • 35
    • 0000557604 scopus 로고
    • A duality theorem for nonlionear programming
    • Wolfe, P. 1961. A duality theorem for nonlionear programming. Quart. Appl. Math. 19 239-244.
    • (1961) Quart. Appl. Math , vol.19 , pp. 239-244
    • Wolfe, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.