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Volumn 42, Issue 1, 2008, Pages 51-67

Tight convex underestimators for C2 -continuous problems: I. univariate functions

Author keywords

BB; Convex envelopes; Convex underestimation; Global optimization; Univariate functions

Indexed keywords

CONVEX UNDERESTIMATION; CONVEX UNDERESTIMATORS; LINEAR SEGMENTS; NOVEL METHODS; PIECEWISE CONVEX; UNIVARIATE FUNCTIONS;

EID: 48449106812     PISSN: 09255001     EISSN: 15732916     Source Type: Journal    
DOI: 10.1007/s10898-008-9287-9     Document Type: Article
Times cited : (27)

References (42)
  • 1
    • 0003086747 scopus 로고    scopus 로고
    • Rigorous convex underestimators for general twice-differentiable problems
    • Adjiman C.S. and Floudas C.A. (1996). Rigorous convex underestimators for general twice-differentiable problems. J. Glob. Optim. 9: 23-40
    • (1996) J. Glob. Optim. , vol.9 , pp. 23-40
    • Adjiman, C.S.1    Floudas, C.A.2
  • 4
    • 2942639818 scopus 로고    scopus 로고
    • A new class of improved convex underestimators for twice continuously differentiable constrained NLPs. J. Glob
    • Akrotirianakis I.G. and Floudas C.A. (2004a). A new class of improved convex underestimators for twice continuously differentiable constrained NLPs. J. Glob. Optim. 30: 367-390
    • (2004) Optim. , vol.30 , pp. 367-390
    • Akrotirianakis, I.G.1    Floudas, C.A.2
  • 5
    • 6944233968 scopus 로고    scopus 로고
    • Computational experience with a new class of convex underestimators: Box-constrained NLP problems
    • Akrotirianakis I.G. and Floudas C.A. (2004b). Computational experience with a new class of convex underestimators: box-constrained NLP problems. J. Glob Optim. 29: 249-264
    • (2004) J. Glob Optim. , vol.29 , pp. 249-264
    • Akrotirianakis, I.G.1    Floudas, C.A.2
  • 6
    • 0020752471 scopus 로고
    • Jointly constrained biconvex programming
    • Al-Khayyal F.A. and Falk J.E. (1983). Jointly constrained biconvex programming. Math. Oper. Res. 8: 273-286
    • (1983) Math. Oper. Res. , vol.8 , pp. 273-286
    • Al-Khayyal, F.A.1    Falk, J.E.2
  • 7
    • 0001327501 scopus 로고
    • αbB: A global optimization method for general constrained nonconvex problems
    • Androulakis I.P., Maranas C.D. and Floudas C.A. (1995). αBB: a global optimization method for general constrained nonconvex problems. J. Glob. Optim. 7: 337-363
    • (1995) J. Glob. Optim. , vol.7 , pp. 337-363
    • Androulakis, I.P.1    Maranas, C.D.2    Floudas, C.A.3
  • 8
    • 18244390168 scopus 로고    scopus 로고
    • Trigonometric convex underestimator for the base functions in Fourier space
    • Caratzoulas S. and Floudas C.A. (2005). Trigonometric convex underestimator for the base functions in Fourier space. J. Optim. Theory Appl. 124: 339-362
    • (2005) J. Optim. Theory Appl. , vol.124 , pp. 339-362
    • Caratzoulas, S.1    Floudas, C.A.2
  • 9
    • 84867937421 scopus 로고    scopus 로고
    • New interval analysis support functions using gradient information in a global minimization algorithm
    • Casado L.G., Martinez J.A., Garcia I. and Sergeyev Y.D. (2003). New interval analysis support functions using gradient information in a global minimization algorithm. J. Glob. Optim. 25: 345-362
    • (2003) J. Glob. Optim. , vol.25 , pp. 345-362
    • Casado, L.G.1    Martinez, J.A.2    Garcia, I.3    Sergeyev, Y.D.4
  • 10
    • 0032069707 scopus 로고    scopus 로고
    • Global optimization in parameter estimation of nonlinear algebraic models via the error-in-variables approach
    • Esposito W.R. and Floudas C.A. (1998). Global optimization in parameter estimation of nonlinear algebraic models via the error-in-variables approach. Indus. Eng. Chem. Res. 35: 1841-1858
    • (1998) Indus. Eng. Chem. Res. , vol.35 , pp. 1841-1858
    • Esposito, W.R.1    Floudas, C.A.2
  • 14
    • 25144487283 scopus 로고    scopus 로고
    • Research challenges, opportunities and synergism in systems engineering and computational biology
    • Floudas C.A. (2005). Research challenges, opportunities and synergism in systems engineering and computational biology. AIChE J. 51: 1872-1884
    • (2005) AIChE J. , vol.51 , pp. 1872-1884
    • Floudas, C.A.1
  • 16
    • 84976486960 scopus 로고    scopus 로고
    • Towards optimal techniques for solving global optimization problems: Symmetry-based approach
    • Torn A., Zilinskas J. (eds.) Springer
    • Floudas, C.A., Kreinovich, V.: Towards optimal techniques for solving global optimization problems: symmetry-based approach. In: Torn A., Zilinskas J. (eds.) Models and Algorithms for Global Optimization, pp. 21-42 Springer (2007a)
    • (2007) Models and Algorithms for Global Optimization , pp. 21-42
    • Floudas, C.A.1    Kreinovich, V.2
  • 17
    • 35148820029 scopus 로고    scopus 로고
    • On the functional form of convex understimators for twice continuously differentiable functions
    • Floudas C.A. and Kreinovich V. (2007b). On the functional form of convex understimators for twice continuously differentiable functions. Optim. Lett. 1: 187-192
    • (2007) Optim. Lett. , vol.1 , pp. 187-192
    • Floudas, C.A.1    Kreinovich, V.2
  • 18
    • 48449106812 scopus 로고    scopus 로고
    • 2 -continuous functions: II Multivariate functions
    • 10.1007/s10898-008-9288-8
    • 2 -continuous functions: II Multivariate functions. J. Glob. Optim. 10.1007/s10898-008-9288-8
    • (2008) J. Glob. Optim.
    • Gounaris, C.E.1    Floudas, C.A.2
  • 19
    • 0035332163 scopus 로고    scopus 로고
    • Global optimization of nonlinear bilevel programming problems
    • Gümüş Z.H. and Floudas C.A. (2001). Global optimization of nonlinear bilevel programming problems. J. Glob. Optim. 20: 1-31
    • (2001) J. Glob. Optim. , vol.20 , pp. 1-31
    • Gümüş, Z.H.1    Floudas, C.A.2
  • 21
    • 0033544453 scopus 로고    scopus 로고
    • Two results on bounding the roots of interval polynomials
    • Hertz D., Adjiman C.S. and Floudas C.A. (1999). Two results on bounding the roots of interval polynomials. Comput. Chem. Eng. 23: 1333-1339
    • (1999) Comput. Chem. Eng. , vol.23 , pp. 1333-1339
    • Hertz, D.1    Adjiman, C.S.2    Floudas, C.A.3
  • 24
    • 84867931017 scopus 로고    scopus 로고
    • Convex envelopes of monomials of odd degree
    • Liberti L. and Pantelides C.C. (2003). Convex envelopes of monomials of odd degree. J. Glob. Optim. 25: 157-168
    • (2003) J. Glob. Optim. , vol.25 , pp. 157-168
    • Liberti, L.1    Pantelides, C.C.2
  • 25
    • 0001203963 scopus 로고
    • Global minimum potential energy conformations of small molecules
    • Maranas C.D. and Floudas C.A. (1994). Global minimum potential energy conformations of small molecules. J. Glob. Optim. 4: 135-170
    • (1994) J. Glob. Optim. , vol.4 , pp. 135-170
    • Maranas, C.D.1    Floudas, C.A.2
  • 26
    • 34249758275 scopus 로고
    • Finding all solutions of nonlinearly constrained systems of equations
    • Maranas C.D. and Floudas C.A. (1995). Finding all solutions of nonlinearly constrained systems of equations. J. Glob. Optim. 7: 143-182
    • (1995) J. Glob. Optim. , vol.7 , pp. 143-182
    • Maranas, C.D.1    Floudas, C.A.2
  • 28
    • 34250381644 scopus 로고
    • Computability of global solutions to factorable nonconvex programs: Part I-Convex underestimating problems
    • McCormick G.P. (1976). Computability of global solutions to factorable nonconvex programs: Part I-Convex underestimating problems. Math. Program. 10: 147-175
    • (1976) Math. Program. , vol.10 , pp. 147-175
    • McCormick, G.P.1
  • 29
    • 0001140188 scopus 로고
    • Decomposition based and branch and bound global optimization approaches for the phase equilibrium problem
    • McDonald C.M. and Floudas C.A. (1994). Decomposition based and branch and bound global optimization approaches for the phase equilibrium problem. J. Glob. Optim. 5: 205-251
    • (1994) J. Glob. Optim. , vol.5 , pp. 205-251
    • McDonald, C.M.1    Floudas, C.A.2
  • 30
    • 0029395174 scopus 로고
    • Global optimization for the phase and chemical equilibrium problem: Application to the NRTL equation
    • McDonald C.M. and Floudas C.A. (1995). Global optimization for the phase and chemical equilibrium problem: application to the NRTL equation. Comput. Chem. Eng. 19: 1111-1141
    • (1995) Comput. Chem. Eng. , vol.19 , pp. 1111-1141
    • McDonald, C.M.1    Floudas, C.A.2
  • 31
    • 0030244667 scopus 로고    scopus 로고
    • GLOPEQ: A new computational tool for the phase and chemical equilibrium problem
    • McDonald C.M. and Floudas C.A. (1997). GLOPEQ: a new computational tool for the phase and chemical equilibrium problem. Comput. Chem. Eng. 21: 1-23
    • (1997) Comput. Chem. Eng. , vol.21 , pp. 1-23
    • McDonald, C.M.1    Floudas, C.A.2
  • 32
    • 4544226754 scopus 로고    scopus 로고
    • Trilinear monomials with positive or negative domains: Facets of the convex and concave envelopes
    • Floudas C.A., Pardalos P.M. (eds.) Kluwer Academic Publishers
    • Meyer, C.A., Floudas, C.A.: Trilinear monomials with positive or negative domains: facets of the convex and concave envelopes. In: Floudas C.A., Pardalos P.M. (eds.) Frontiers in Global Optimization. Kluwer Academic Publishers (2003)
    • (2003) Frontiers in Global Optimization
    • Meyer, C.A.1    Floudas, C.A.2
  • 33
    • 4544251356 scopus 로고    scopus 로고
    • Trilinear monomials with mixed sign domains: Facets of the convex and concave envelopes
    • Meyer C.A. and Floudas C.A. (2004). Trilinear monomials with mixed sign domains: facets of the convex and concave envelopes. J. Glob. Optim. 29: 125-155
    • (2004) J. Glob. Optim. , vol.29 , pp. 125-155
    • Meyer, C.A.1    Floudas, C.A.2
  • 34
    • 25144488748 scopus 로고    scopus 로고
    • Convex underestimation of twice continuously differentiable functions by piecewise quadratic perturbation: Spline αbB underestimators
    • Meyer C.A. and Floudas C.A. (2005). Convex underestimation of twice continuously differentiable functions by piecewise quadratic perturbation: spline αBB underestimators. J. Glob. Optim. 32: 221-258
    • (2005) J. Glob. Optim. , vol.32 , pp. 221-258
    • Meyer, C.A.1    Floudas, C.A.2
  • 35
    • 33645563984 scopus 로고    scopus 로고
    • Global optimization of a combinatorially complex generalized pooling problem.
    • Meyer C.A. and Floudas C.A. (2006). Global optimization of a combinatorially complex generalized pooling problem. AIChE J. 52: 1027-1037
    • (2006) AIChE J. , vol.52 , pp. 1027-1037
    • Meyer, C.A.1    Floudas, C.A.2
  • 37
    • 0035306565 scopus 로고    scopus 로고
    • Analysis of bounds for multilinear functions
    • Ryoo H.S. and Sahinidis N.V. (2001). Analysis of bounds for multilinear functions. J. Glob. Optim. 19: 403-424
    • (2001) J. Glob. Optim. , vol.19 , pp. 403-424
    • Ryoo, H.S.1    Sahinidis, N.V.2
  • 39
    • 0035364533 scopus 로고    scopus 로고
    • Semidefinite relaxations of fractional programs via novel convexification techniques
    • Tawarmalani M. and Sahinidis N.V. (2001). Semidefinite relaxations of fractional programs via novel convexification techniques. J. Glob. Optim. 20: 137-158
    • (2001) J. Glob. Optim. , vol.20 , pp. 137-158
    • Tawarmalani, M.1    Sahinidis, N.V.2
  • 41
    • 33751003528 scopus 로고    scopus 로고
    • Convex extensions and envelopes of lower semi-continuous functions
    • Tawarmalani M. and Sahinidis N.V. (2002b). Convex extensions and envelopes of lower semi-continuous functions. Math. Program. 93: 247-263
    • (2002) Math. Program. , vol.93 , pp. 247-263
    • Tawarmalani, M.1    Sahinidis, N.V.2


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