메뉴 건너뛰기




Volumn 8, Issue 1, 1998, Pages 105-122

On some properties of quadratic programs with a convex quadratic constraint

Author keywords

Merit function; Quadratic function; 2 norm constraint

Indexed keywords


EID: 0032326764     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623494278049     Document Type: Article
Times cited : (40)

References (42)
  • 2
    • 0015200767 scopus 로고
    • Direct methods for solving symmetric indefinite systems of linear equations
    • J. BUNCH AND B. PARLETT, Direct methods for solving symmetric indefinite systems of linear equations, SIAM J. Numer. Anal., 8 (1971), pp. 639-655.
    • (1971) SIAM J. Numer. Anal. , vol.8 , pp. 639-655
    • Bunch, J.1    Parlett, B.2
  • 3
    • 0000761866 scopus 로고
    • Computing a trust region step for a penalty function
    • T. F. COLEMAN AND C. HEMPEL, Computing a trust region step for a penalty function, SIAM J. Sci. Statist. Comput., 11 (1990), pp. 180-201.
    • (1990) SIAM J. Sci. Statist. Comput. , vol.11 , pp. 180-201
    • Coleman, T.F.1    Hempel, C.2
  • 5
    • 0020763823 scopus 로고
    • Truncated-Newton methods algorithms for large-scale unconstrained optimization
    • R. DEMBO AND T. STEIHAUG, Truncated-Newton methods algorithms for large-scale unconstrained optimization, Math. Programming, 26 (1983), pp. 190-212.
    • (1983) Math. Programming , vol.26 , pp. 190-212
    • Dembo, R.1    Steihaug, T.2
  • 6
    • 0022796667 scopus 로고
    • An exact penalty method with global convergence properties for nonlinear programming problems
    • G. DI PILLO AND L. GRIPPO, An exact penalty method with global convergence properties for nonlinear programming problems, Math. Programming, 36 (1986), pp. 1-18.
    • (1986) Math. Programming , vol.36 , pp. 1-18
    • Di Pillo, G.1    Grippo, L.2
  • 7
    • 0024768569 scopus 로고
    • Exact penalty functions in constrained optimization
    • G. DI PILLO AND L. GRIPPO, Exact penalty functions in constrained optimization, SIAM J. Control Optim., 27 (1989), pp. 1333-1360.
    • (1989) SIAM J. Control Optim. , vol.27 , pp. 1333-1360
    • Di Pillo, G.1    Grippo, L.2
  • 8
    • 21844493148 scopus 로고
    • Quadratically and superlinear convergent algorithms for the solution of inequality constrained optimization problems
    • F. FACCHINEI AND S. LUCIDI, Quadratically and superlinear convergent algorithms for the solution of inequality constrained optimization problems, J. Optim. Theory Appl., 85 (1985), pp. 265-289.
    • (1985) J. Optim. Theory Appl. , vol.85 , pp. 265-289
    • Facchinei, F.1    Lucidi, S.2
  • 9
    • 0003336489 scopus 로고
    • A class of methods for nonlinear programming with termination and convergence properties
    • J. Abadie, ed., North-Holland, Amsterdam
    • R. E. FLETCHER, A class of methods for nonlinear programming with termination and convergence properties, in Integer and Nonlinear Programming, J. Abadie, ed., North-Holland, Amsterdam, 1979, pp. 157-173.
    • (1979) Integer and Nonlinear Programming , pp. 157-173
    • Fletcher, R.E.1
  • 10
    • 0000106422 scopus 로고
    • Computing modified newton directions using a partial Cholesky factorization
    • A. FORSGREN, P. GILL, AND W. MURRAY, Computing modified Newton directions using a partial Cholesky factorization, SIAM J. Sci. Comput., 16 (1995), pp. 139-150.
    • (1995) SIAM J. Sci. Comput. , vol.16 , pp. 139-150
    • Forsgren, A.1    Gill, P.2    Murray, W.3
  • 11
    • 0001046905 scopus 로고
    • On the stationary values of a second-degree polynomial on the unit sphere
    • G. FORSYTHE AND G. GOLUB, On the stationary values of a second-degree polynomial on the unit sphere. J. Soc. Indust. Appl. Math., 13 (1965), pp. 1050-1068.
    • (1965) J. Soc. Indust. Appl. Math. , vol.13 , pp. 1050-1068
    • Forsythe, G.1    Golub, G.2
  • 12
    • 0000955796 scopus 로고
    • Computing optimal locally constrained steps
    • D. M. GAY, Computing optimal locally constrained steps, SIAM J. Sci. Statist. Comput., 2 (1981), pp. 186-197.
    • (1981) SIAM J. Sci. Statist. Comput. , vol.2 , pp. 186-197
    • Gay, D.M.1
  • 13
    • 0018522912 scopus 로고
    • A multiplier method with automatic limitation of penalty growth
    • T. GLAD AND E. POLAK, A multiplier method with automatic limitation of penalty growth, Math. Programming, 17 (1979), pp. 140-155.
    • (1979) Math. Programming , vol.17 , pp. 140-155
    • Glad, T.1    Polak, E.2
  • 14
    • 0022766519 scopus 로고
    • A nonmonotone line search technique for Newton's method
    • L. GRIPPO, F. LAMPARIELLO, AND S. LUCIDI, A nonmonotone line search technique for Newton's method, SIAM J. Numer. Anal., 23 (1986), pp. 707-716.
    • (1986) SIAM J. Numer. Anal. , vol.23 , pp. 707-716
    • Grippo, L.1    Lampariello, F.2    Lucidi, S.3
  • 15
    • 0000843862 scopus 로고
    • A truncated Newton method with nonmonotone linesearch for unconstrained optimization
    • L. GRIPPO, F. LAMPARIELLO, AND S. LUCIDI, A truncated Newton method with nonmonotone linesearch for unconstrained optimization, J. Optim. Theory Appl., 60 (1989), pp. 401-419.
    • (1989) J. Optim. Theory Appl. , vol.60 , pp. 401-419
    • Grippo, L.1    Lampariello, F.2    Lucidi, S.3
  • 16
    • 84948343716 scopus 로고
    • A differentiable exact penalty function for bound constrained quadratic programming problems
    • L. GRIPPO AND S. LUCIDI, A differentiable exact penalty function for bound constrained quadratic programming problems, Optimization, 22 (1991), pp. 557-578.
    • (1991) Optimization , vol.22 , pp. 557-578
    • Grippo, L.1    Lucidi, S.2
  • 17
    • 0028425178 scopus 로고
    • On the solution of a two ball trust region subproblem
    • M. HEINKENSCHLOSS, On the solution of a two ball trust region subproblem, Math. Programming, 64 (1994), pp. 249-276.
    • (1994) Math. Programming , vol.64 , pp. 249-276
    • Heinkenschloss, M.1
  • 18
    • 0014604308 scopus 로고
    • Multiplier and gradient methods
    • M. HESTENES, Multiplier and gradient methods, J. Optim. Theory Appl., 4 (1969), pp. 303-320.
    • (1969) J. Optim. Theory Appl. , vol.4 , pp. 303-320
    • Hestenes, M.1
  • 19
    • 0039924875 scopus 로고
    • A continuous approach to compute upper bounds in quadratic maximization problems with integer constraints
    • C. A. Floudas and P. M. Pardalos, eds., Princeton University Press, Princeton, NJ
    • A. KAMATH AND N. KARMARKAR, A continuous approach to compute upper bounds in quadratic maximization problems with integer constraints, in Recent Advances in Global Optimization, C. A. Floudas and P. M. Pardalos, eds., Princeton University Press, Princeton, NJ, 1991, pp. 125-140.
    • (1991) Recent Advances in Global Optimization , pp. 125-140
    • Kamath, A.1    Karmarkar, N.2
  • 20
    • 0039551804 scopus 로고
    • Fast algorithms for convex quadratic programming and multicommodity flows
    • ACM, New York
    • S. KAPOOR AND P. VAIDYA, Fast algorithms for convex quadratic programming and multicommodity flows, in Proc. 18th Annual ACM Symp. Theory Comput., ACM, New York, 1986, pp. 147-159.
    • (1986) Proc. 18th Annual ACM Symp. Theory Comput. , pp. 147-159
    • Kapoor, S.1    Vaidya, P.2
  • 22
    • 34249928512 scopus 로고
    • An interior point algorithm to solve computationally difficult set covering problems
    • N. KARMARKAR, M. G. C. RESENDE, AND K. RAMAKRISHNAN, An interior point algorithm to solve computationally difficult set covering problems, Math. Programming, 52 (1991), pp. 597-618.
    • (1991) Math. Programming , vol.52 , pp. 597-618
    • Karmarkar, N.1    Resende, M.G.C.2    Ramakrishnan, K.3
  • 23
    • 0030303843 scopus 로고    scopus 로고
    • Differentiable piecewise quadratic exact penalty functions for quadratic programs with simple bound constraints
    • W. LI, Differentiable piecewise quadratic exact penalty functions for quadratic programs with simple bound constraints, SIAM J. Optim., 6 (1996), pp. 299-315.
    • (1996) SIAM J. Optim. , vol.6 , pp. 299-315
    • Li, W.1
  • 24
    • 85033893498 scopus 로고    scopus 로고
    • Tech. Report 36.96, Dipartimento di Informatica e Sistemistica, Università di Roma "La Sapienza," Roma, Italy
    • S. LUCIDI AND L. PALAGI, A class of algorithms for large scale trust region problems, Tech. report 36.96, Dipartimento di Informatica e Sistemistica, Università di Roma "La Sapienza," Roma, Italy, 1996.
    • (1996) A Class of Algorithms for Large Scale Trust Region Problems
    • Lucidi, S.1    Palagi, L.2
  • 26
    • 0000442245 scopus 로고
    • Local minimizers of quadratic functions on Euclidean balls and spheres
    • J. MARTÍNEZ, Local minimizers of quadratic functions on Euclidean balls and spheres, SIAM J. Optim., 4 (1994), pp. 159-176.
    • (1994) SIAM J. Optim. , vol.4 , pp. 159-176
    • Martínez, J.1
  • 27
    • 34249768673 scopus 로고
    • Trust region algorithms on arbitrary domains
    • J. MARTÍNEZ AND S. A. SANTOS, Trust region algorithms on arbitrary domains, Math. Programming, 68 (1995), pp. 267-302.
    • (1995) Math. Programming , vol.68 , pp. 267-302
    • Martínez, J.1    Santos, S.A.2
  • 28
    • 0027901827 scopus 로고
    • Generalization of the trust region problem
    • J. MORÉ, Generalization of the trust region problem, Optimization Methods and Software, 2 (1993), pp. 189-209.
    • (1993) Optimization Methods and Software , vol.2 , pp. 189-209
    • Moré, J.1
  • 29
    • 0001818862 scopus 로고
    • On the use of directions of negative curvature in a modified Newton method
    • J. MORÉ AND D. SORENSEN, On the use of directions of negative curvature in a modified Newton method, Math. Programming, 16 (1979), pp. 1-20.
    • (1979) Math. Programming , vol.16 , pp. 1-20
    • Moré, J.1    Sorensen, D.2
  • 31
    • 0001927695 scopus 로고
    • Algorithms for the solution of quadratic knapsack problems
    • P. M. PARDALOS, Y. YE, AND C.-G. HAN, Algorithms for the solution of quadratic knapsack problems, Linear Algebra Appl., 25 (1991), pp. 69-91.
    • (1991) Linear Algebra Appl. , vol.25 , pp. 69-91
    • Pardalos, P.M.1    Ye, Y.2    Han, C.-G.3
  • 32
    • 0002380692 scopus 로고
    • A method for nonlinear constraints in minimization problem
    • R. Fletcher, ed., Academic Press, New York
    • M. J. D. POWELL, A method for nonlinear constraints in minimization problem, in Optimization, R. Fletcher, ed., Academic Press, New York, 1969, pp. 283-298.
    • (1969) Optimization , pp. 283-298
    • Powell, M.J.D.1
  • 35
    • 0001382978 scopus 로고
    • Newton's method with a model trust region modification
    • D. C. SORENSEN, Newton's method with a model trust region modification, SIAM J. Numer. Anal., 19 (1982), pp. 409-426.
    • (1982) SIAM J. Numer. Anal. , vol.19 , pp. 409-426
    • Sorensen, D.C.1
  • 37
    • 0002633896 scopus 로고
    • Towards an efficient sparsity exploiting Newton method for minimization
    • I. S. Duff, ed., Academic Press, London
    • P. TOINT, Towards an efficient sparsity exploiting Newton method for minimization, in Sparse Matrices and Their Uses, I. S. Duff, ed., Academic Press, London, 1981, pp. 57-88.
    • (1981) Sparse Matrices and Their Uses , pp. 57-88
    • Toint, P.1
  • 40
    • 0008975068 scopus 로고
    • A new complexity result on minimization of a quadratic function with a sphere constraint
    • C. A. Floudas and P. M. Pardalos, eds., Princeton University Press, Princeton, NJ
    • Y. YE, A new complexity result on minimization of a quadratic function with a sphere constraint, in Recent Advances in Global Optimization, C. A. Floudas and P. M. Pardalos, eds., Princeton University Press, Princeton, NJ, 1991, pp. 19-31.
    • (1991) Recent Advances in Global Optimization , pp. 19-31
    • Ye, Y.1
  • 41
    • 34249839449 scopus 로고
    • On affine scaling algorithms for nonconvex quadratic programming
    • Y. YE, On affine scaling algorithms for nonconvex quadratic programming, Math. Programming, 56 (1992), pp. 285-300.
    • (1992) Math. Programming , vol.56 , pp. 285-300
    • Ye, Y.1
  • 42
    • 0024683802 scopus 로고
    • An extension of Karmarkar's projective algorithm for convex quadratic programming
    • Y. YE AND E. TSE, An extension of Karmarkar's projective algorithm for convex quadratic programming, Math. Programming, 44 (1989), pp. 157-179.
    • (1989) Math. Programming , vol.44 , pp. 157-179
    • Ye, Y.1    Tse, E.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.