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Volumn 153, Issue 1, 2007, Pages 257-296

Complexity and algorithms for nonlinear optimization problems

Author keywords

Convex network flow; Lower bounds on complexity; Nonlinear optimization; Strongly polynomial algorithms

Indexed keywords


EID: 34250213217     PISSN: 02545330     EISSN: 15729338     Source Type: Journal    
DOI: 10.1007/s10479-007-0172-6     Document Type: Article
Times cited : (81)

References (77)
  • 2
    • 0021432711 scopus 로고
    • A parametric algorithm for the convex cost network flow and related problems
    • Ahuja, R. K., Batra, J. L., & Gupta, S. K. (1984). A parametric algorithm for the convex cost network flow and related problems. European Journal of Operational Research, 16, 222-235.
    • (1984) European Journal of Operational Research , vol.16 , pp. 222-235
    • Ahuja, R.K.1    Batra, J.L.2    Gupta, S.K.3
  • 3
    • 0042266794 scopus 로고    scopus 로고
    • Solving the convex cost integer dual network flow problem
    • Ahuja, R. K., Hochbaum, D. S., & Orlin, J. B. (2003). Solving the convex cost integer dual network flow problem. Management Science, 49, 950-964.
    • (2003) Management Science , vol.49 , pp. 950-964
    • Ahuja, R.K.1    Hochbaum, D.S.2    Orlin, J.B.3
  • 4
    • 21044452195 scopus 로고    scopus 로고
    • A cut based algorithm for the nonlinear dual of the minimum cost network flow problem
    • Ahuja, R. K., Hochbaum, D. S., & Orlin, J. B. (2004). A cut based algorithm for the nonlinear dual of the minimum cost network flow problem. Algorithmica, 39, 189-208.
    • (2004) Algorithmica , vol.39 , pp. 189-208
    • Ahuja, R.K.1    Hochbaum, D.S.2    Orlin, J.B.3
  • 7
    • 0025470367 scopus 로고
    • Efficient integer optimization algorithms for optimal coordination of capacitors and regulators
    • Baldick, R., & Wu, F. F. (1990). Efficient integer optimization algorithms for optimal coordination of capacitors and regulators. IEEE Transactions on Power Systems, 5, 805-812.
    • (1990) IEEE Transactions on Power Systems , vol.5 , pp. 805-812
    • Baldick, R.1    Wu, F.F.2
  • 8
    • 0022532078 scopus 로고
    • A solvable case of quadratic 0-1 programming
    • Barahona, F. (1986). A solvable case of quadratic 0-1 programming. Discrete Applied Mathematics, 13, 23-28.
    • (1986) Discrete Applied Mathematics , vol.13 , pp. 23-28
    • Barahona, F.1
  • 11
    • 0021479943 scopus 로고
    • An O(n) algorithm for quadratic knapsack problems
    • Brucker, P. (1984). An O(n) algorithm for quadratic knapsack problems. Operations Research Letters, 3, 163-166.
    • (1984) Operations Research Letters , vol.3 , pp. 163-166
    • Brucker, P.1
  • 12
    • 0026742679 scopus 로고
    • On an instance of the inverse shortest paths problem
    • Burton, D., & Toint, Ph. L. (1992). On an instance of the inverse shortest paths problem. Mathematical Programming, 53, 45-61.
    • (1992) Mathematical Programming , vol.53 , pp. 45-61
    • Burton, D.1    Toint, P.L.2
  • 13
    • 0028766968 scopus 로고
    • On the use of an inverse shortest paths algorithm for recovering linearly correlated costs
    • Burton, D., & Toint, Ph. L. (1994). On the use of an inverse shortest paths algorithm for recovering linearly correlated costs. Mathematical Programming, 63, 1-22.
    • (1994) Mathematical Programming , vol.63 , pp. 1-22
    • Burton, D.1    Toint, P.L.2
  • 15
    • 26444460409 scopus 로고
    • A strongly polynomial algorithm for the quadratic transportation problem with fixed number of suppliers
    • Cosares, S., & Hochbaum, D. S. (1994). A strongly polynomial algorithm for the quadratic transportation problem with fixed number of suppliers. Mathematics of Operations Research, 19, 94-111.
    • (1994) Mathematics of Operations Research , vol.19 , pp. 94-111
    • Cosares, S.1    Hochbaum, D.S.2
  • 17
    • 0002776326 scopus 로고
    • Mathematical programming and electrical networks
    • New York: Technology Press and Wiley
    • Dennis, J. B. (1959). Mathematical programming and electrical networks. In Technology press research monographs (pp. 74-75). New York: Technology Press and Wiley.
    • (1959) Technology press research monographs , pp. 74-75
    • Dennis, J.B.1
  • 18
    • 0015330635 scopus 로고
    • Theoretical improvements in algorithmic efficiency for network flow problems
    • Edmonds, J., & Karp, R. M. (1972). Theoretical improvements in algorithmic efficiency for network flow problems. Journal of ACM, 19, 248-264.
    • (1972) Journal of ACM , vol.19 , pp. 248-264
    • Edmonds, J.1    Karp, R.M.2
  • 20
    • 0022816715 scopus 로고
    • The greedy procedure for resource allocation problems: Necessary and sufficient conditions for optimality
    • Federgruen, A., & Groenevelt, H. ( 1986a). The greedy procedure for resource allocation problems: Necessary and sufficient conditions for optimality. Operations Research, 34, 909-918.
    • (1986) Operations Research , vol.34 , pp. 909-918
    • Federgruen, A.1    Groenevelt, H.2
  • 21
    • 0022677324 scopus 로고
    • Optimal flows in networks with multiple sources and sinks, with applications to oil and gas lease investment programs
    • Federgruen, A., & Groenevelt, H. (1986b). Optimal flows in networks with multiple sources and sinks, with applications to oil and gas lease investment programs. Operations Research, 34, 218-225.
    • (1986) Operations Research , vol.34 , pp. 218-225
    • Federgruen, A.1    Groenevelt, H.2
  • 22
    • 0020120231 scopus 로고
    • The complexity of selection and rankings in X + Y and matrices with sorted columns
    • Frederickson, G. N., & Johnson, D. B. (1982). The complexity of selection and rankings in X + Y and matrices with sorted columns. Journal of Computing System Science, 24, 197-208.
    • (1982) Journal of Computing System Science , vol.24 , pp. 197-208
    • Frederickson, G.N.1    Johnson, D.B.2
  • 23
    • 0024084926 scopus 로고
    • A simplex algorithm for piecewise-linear programming: Finiteness, feasibility and degeneracy
    • Fourer, R. (1988). A simplex algorithm for piecewise-linear programming: Finiteness, feasibility and degeneracy. Mathematical Programming, 41, 281-316.
    • (1988) Mathematical Programming , vol.41 , pp. 281-316
    • Fourer, R.1
  • 24
    • 84972520507 scopus 로고
    • A theorem of flows in networks
    • Gale, D. (1957). A theorem of flows in networks. Pacific Journal of Mathematics, 7, 1073-1082.
    • (1957) Pacific Journal of Mathematics , vol.7 , pp. 1073-1082
    • Gale, D.1
  • 27
    • 0024090156 scopus 로고
    • A new approach to the maximum flow problem
    • Goldberg, A. V., & Tarjan, R. E. (1988). A new approach to the maximum flow problem. Journal of the ACM, 35, 921-940.
    • (1988) Journal of the ACM , vol.35 , pp. 921-940
    • Goldberg, A.V.1    Tarjan, R.E.2
  • 28
    • 0025449182 scopus 로고
    • Some proximity and sensitivity results in quadratic integer programming
    • Granot, F., & Skorin-Kapov, J. (1990). Some proximity and sensitivity results in quadratic integer programming. Mathematical Programming, 47, 259-268.
    • (1990) Mathematical Programming , vol.47 , pp. 259-268
    • Granot, F.1    Skorin-Kapov, J.2
  • 29
    • 0002499479 scopus 로고
    • Minimum concave cost network flow problems: Applications, complexity, and algorithms
    • Guisewite, G., & Pardalos, P. M. (1990). Minimum concave cost network flow problems: Applications, complexity, and algorithms. Annals of Operations Research, 25, 75-100.
    • (1990) Annals of Operations Research , vol.25 , pp. 75-100
    • Guisewite, G.1    Pardalos, P.M.2
  • 32
    • 26444505068 scopus 로고
    • Polynomial algorithms for convex network optimization
    • D. Du, M. Pardalos Eds, Singapore: World Scientific
    • Hochbaum, D. S. (1993). Polynomial algorithms for convex network optimization. In D. Du, M. Pardalos (Eds.), Network optimization problems: algorithms, complexity and applications (pp. 63-92). Singapore: World Scientific.
    • (1993) Network optimization problems: Algorithms, complexity and applications , pp. 63-92
    • Hochbaum, D.S.1
  • 33
    • 0000860218 scopus 로고
    • Lower and upper bounds for allocation problems
    • Hochbaum, D. S. (1994). Lower and upper bounds for allocation problems. Mathematics of Operations Research, 19, 390-409.
    • (1994) Mathematics of Operations Research , vol.19 , pp. 390-409
    • Hochbaum, D.S.1
  • 35
    • 84873011783 scopus 로고    scopus 로고
    • Hochbaum, D. S. (1998). The pseudoflow algorithm for the maximum flow problem. Manuscript, UC Berke-ley, revised 2003. Extended abstract in: Boyd & Rios-Mercado (Eds.), Lecture notes in computer science: 1412. The pseudoflow algorithm and the pseudoflow-based simplex for the maximum flow problem. Proceedings of IPCO98 (pp. 325-337), Bixby, June 1998. New York: Springer.
    • Hochbaum, D. S. (1998). The pseudoflow algorithm for the maximum flow problem. Manuscript, UC Berke-ley, revised 2003. Extended abstract in: Boyd & Rios-Mercado (Eds.), Lecture notes in computer science: Vol. 1412. The pseudoflow algorithm and the pseudoflow-based simplex for the maximum flow problem. Proceedings of IPCO98 (pp. 325-337), Bixby, June 1998. New York: Springer.
  • 36
    • 0008821575 scopus 로고    scopus 로고
    • An efficient algorithm for image segmentation, Markov random fields and related problems
    • Hochbaum, D. S. (2001). An efficient algorithm for image segmentation, Markov random fields and related problems. Journal of the. ACM, 48, 686-701.
    • (2001) Journal of the. ACM , vol.48 , pp. 686-701
    • Hochbaum, D.S.1
  • 38
    • 3142618986 scopus 로고    scopus 로고
    • Efficient algorithms for the inverse spanning tree problem
    • Hochbaum, D. S. (2003). Efficient algorithms for the inverse spanning tree problem. Operations Research, 51, 785-797.
    • (2003) Operations Research , vol.51 , pp. 785-797
    • Hochbaum, D.S.1
  • 40
    • 0001687035 scopus 로고
    • About strongly polynomial time algorithms for quadratic optimization over submodular constraints
    • Hochbaum, D. S., & Hong, S. P. (1995). About strongly polynomial time algorithms for quadratic optimization over submodular constraints. Mathematical Programming, 69, 269-309.
    • (1995) Mathematical Programming , vol.69 , pp. 269-309
    • Hochbaum, D.S.1    Hong, S.P.2
  • 41
    • 0030304778 scopus 로고    scopus 로고
    • On the complexity of the production-transportation problem
    • Hochbaum, D. S., & Hong, S. P. (1996). On the complexity of the production-transportation problem. SIAM Journal on Optimization, 6, 250-264.
    • (1996) SIAM Journal on Optimization , vol.6 , pp. 250-264
    • Hochbaum, D.S.1    Hong, S.P.2
  • 43
    • 26444594502 scopus 로고
    • The empirical performance of a polynomial algorithm for constrained nonlinear optimization
    • Hochbaum, D. S., & Seshadri, S. (1993). The empirical performance of a polynomial algorithm for constrained nonlinear optimization. Annals of Operations Research, 43, 229-248.
    • (1993) Annals of Operations Research , vol.43 , pp. 229-248
    • Hochbaum, D.S.1    Seshadri, S.2
  • 44
    • 0025496223 scopus 로고
    • Convex separable optimization is not much harder than linear optimization
    • Hochbaum, D. S., & Shanthikumar, J. G. (1990). Convex separable optimization is not much harder than linear optimization. Journal of the ACM, 37, 843-862.
    • (1990) Journal of the ACM , vol.37 , pp. 843-862
    • Hochbaum, D.S.1    Shanthikumar, J.G.2
  • 45
    • 34249840416 scopus 로고
    • A polynomial algorithm for an integer quadratic nonseparable transportation problem
    • Hochbaum, D. S., Shamir, R., & Shanthikumar, J. G. (1992). A polynomial algorithm for an integer quadratic nonseparable transportation problem. Mathematical Programming, 55, 359-372.
    • (1992) Mathematical Programming , vol.55 , pp. 359-372
    • Hochbaum, D.S.1    Shamir, R.2    Shanthikumar, J.G.3
  • 46
    • 84872998171 scopus 로고    scopus 로고
    • Hoffman, A. J. (1960). Some recent applications of the theory of linear inequalities to extremal combinatorial analysis. In R. Bellman, M. Hall Jr. (Eds.), Proceedings of Symposia in Applied Mathematics: X. Combinatorial analysis (pp. 113-127). Providence: American mathematical Society.
    • Hoffman, A. J. (1960). Some recent applications of the theory of linear inequalities to extremal combinatorial analysis. In R. Bellman, M. Hall Jr. (Eds.), Proceedings of Symposia in Applied Mathematics: Vol. X. Combinatorial analysis (pp. 113-127). Providence: American mathematical Society.
  • 49
    • 0003601787 scopus 로고
    • Optimal flow through networks
    • Technical report No. 8, Operations research Center, MIT, Cambridge
    • Jewell, W. S. (1958). Optimal flow through networks. Technical report No. 8, Operations research Center, MIT, Cambridge.
    • (1958)
    • Jewell, W.S.1
  • 51
    • 0031209772 scopus 로고    scopus 로고
    • Polynomial methods for separable convex optimization in unimodular linear spaces with applications
    • Karzanov, A. V., & McCormick, S. T. (1997). Polynomial methods for separable convex optimization in unimodular linear spaces with applications. SIAM Journal on Computing, 26, 1245-1275.
    • (1997) SIAM Journal on Computing , vol.26 , pp. 1245-1275
    • Karzanov, A.V.1    McCormick, S.T.2
  • 52
    • 0242344362 scopus 로고
    • The an of computer programming
    • Reading: Addison Wesley
    • Knuth, D. (1973). The an of computer programming: Vol. 3. Sorting and searching. Reading: Addison Wesley.
    • (1973) Sorting and searching , vol.3
    • Knuth, D.1
  • 53
  • 54
    • 0141968029 scopus 로고
    • (Translated in Soviet Mathematics Doklady 20 (1979), 1108-1111).
    • (1979) Soviet Mathematics Doklady , vol.20 , pp. 1108-1111
  • 55
    • 0001099866 scopus 로고
    • Fast approximation algorithms for knapsack problems
    • Lawler, E. (1979). Fast approximation algorithms for knapsack problems. Mathematics of Operations Research, 4, 339-356.
    • (1979) Mathematics of Operations Research , vol.4 , pp. 339-356
    • Lawler, E.1
  • 56
    • 0026140431 scopus 로고
    • Lower bounds for computations with the floor operation
    • Mansour, Y., Schieber, B., & Tiwari, P. (1991). Lower bounds for computations with the floor operation. SIAM Journal on Computing, 20, 315-327.
    • (1991) SIAM Journal on Computing , vol.20 , pp. 315-327
    • Mansour, Y.1    Schieber, B.2    Tiwari, P.3
  • 57
    • 0027602304 scopus 로고
    • Linear time algorithms for some separable quadratic programming problems
    • Megiddo, N., & Tamir, A. (1993). Linear time algorithms for some separable quadratic programming problems. Operations Research Letters, 13, 203-211.
    • (1993) Operations Research Letters , vol.13 , pp. 203-211
    • Megiddo, N.1    Tamir, A.2
  • 58
    • 0021608332 scopus 로고
    • A polynomial algorithm for minimum quadratic cost flow problems
    • Minoux, M. (1984). A polynomial algorithm for minimum quadratic cost flow problems. European Journal of Operational Research, 18, 377-387.
    • (1984) European Journal of Operational Research , vol.18 , pp. 377-387
    • Minoux, M.1
  • 59
    • 0020722506 scopus 로고
    • Solving integer minimum cost flows with separable convex cost objective polynomially
    • Minoux, M. (1986). Solving integer minimum cost flows with separable convex cost objective polynomially. Mathematical Programming Study, 26, 237-239.
    • (1986) Mathematical Programming Study , vol.26 , pp. 237-239
    • Minoux, M.1
  • 61
    • 0024665753 scopus 로고
    • Interior path following primal-dual algorithms. Part II: Convex quadratic programming
    • Monteiro, R. D. C., & Adler (1989). Interior path following primal-dual algorithms. Part II: Convex quadratic programming. Mathematical Programming, 44, 43-66.
    • (1989) Mathematical Programming , vol.44 , pp. 43-66
    • Monteiro, R.D.C.1    Adler2
  • 62
    • 4043154807 scopus 로고    scopus 로고
    • On Hochbaum's proximity-scaling algorithm for the general resource allocation problem
    • Moriguchi, S., & Shioura, A. (2004). On Hochbaum's proximity-scaling algorithm for the general resource allocation problem. Mathematics of Operations Research, 29, 394-397.
    • (2004) Mathematics of Operations Research , vol.29 , pp. 394-397
    • Moriguchi, S.1    Shioura, A.2
  • 65
    • 0016972463 scopus 로고
    • Maximal closure of a graph and applications to combinatorial problems
    • Picard, J. C. (1976). Maximal closure of a graph and applications to combinatorial problems. Management Science, 22, 1268-1272.
    • (1976) Management Science , vol.22 , pp. 1268-1272
    • Picard, J.C.1
  • 66
    • 0028399778 scopus 로고
    • Efficient algorithms for minimum-cost flow problems with piecewise-linear convex costs
    • Pinto, Y., & Shamir, R. (1994). Efficient algorithms for minimum-cost flow problems with piecewise-linear convex costs. Algorithmica, 11(3), 256-276.
    • (1994) Algorithmica , vol.11 , Issue.3 , pp. 256-276
    • Pinto, Y.1    Shamir, R.2
  • 67
    • 0003030458 scopus 로고
    • Parametric flows, Weighted means of cuts, and fractional combinatorial optimization
    • P.M. Pardalos Ed, Singapore: World Scientific
    • Radzik, T. (1993). Parametric flows, Weighted means of cuts, and fractional combinatorial optimization. In P.M. Pardalos (Ed.), Complexity in numerical optimization (pp. 351-386). Singapore: World Scientific.
    • (1993) Complexity in numerical optimization , pp. 351-386
    • Radzik, T.1
  • 68
    • 38249035936 scopus 로고
    • On the worst case arithmetic complexity of approximation zeroes of polynomials
    • Renegar, J. (1987). On the worst case arithmetic complexity of approximation zeroes of polynomials. Journal of Complexity, 3, 90-113.
    • (1987) Journal of Complexity , vol.3 , pp. 90-113
    • Renegar, J.1
  • 70
    • 0001223006 scopus 로고
    • Computationally related Problems
    • Sahni, S. (1974). Computationally related Problems. SIAM Journal on Computing, 3, 262-279.
    • (1974) SIAM Journal on Computing , vol.3 , pp. 262-279
    • Sahni, S.1
  • 71
    • 0022659074 scopus 로고    scopus 로고
    • Computational complexity: On the geometry of polynomials and a theory of cost, II
    • Shub, M., & Smale, S. (1996). Computational complexity: On the geometry of polynomials and a theory of cost, II. SIAM Journal on Computing, 15, 145-161.
    • (1996) SIAM Journal on Computing , vol.15 , pp. 145-161
    • Shub, M.1    Smale, S.2
  • 72
    • 84873004487 scopus 로고    scopus 로고
    • Sun, J., Tsai, K. -H., & Qi, L. (1993). A simplex method for network programs with convex separable piecewise linear costs and its application to stochastic transshipment problems. In D. Du & P. M. Pardalos (Eds.), Network optimization problems: Algorithms, complexity and applications (pp. 283-300). Singapore: World Scientific.
    • Sun, J., Tsai, K. -H., & Qi, L. (1993). A simplex method for network programs with convex separable piecewise linear costs and its application to stochastic transshipment problems. In D. Du & P. M. Pardalos (Eds.), Network optimization problems: Algorithms, complexity and applications (pp. 283-300). Singapore: World Scientific.
  • 73
    • 0027555305 scopus 로고
    • A strongly polynomial algorithm for minimum convex separable quadratic cost flow problems on series-parallel networks
    • Tamir, A. (1993). A strongly polynomial algorithm for minimum convex separable quadratic cost flow problems on series-parallel networks. Mathematical Programming, 59, 117-132.
    • (1993) Mathematical Programming , vol.59 , pp. 117-132
    • Tamir, A.1
  • 74
    • 51249170715 scopus 로고
    • A strongly polynomial minimum cost circulation algorithm
    • Tardos, E. (1985). A strongly polynomial minimum cost circulation algorithm. Combinatorica, 5, 247-255.
    • (1985) Combinatorica , vol.5 , pp. 247-255
    • Tardos, E.1
  • 75
    • 0022672734 scopus 로고
    • A strongly polynomial algorithm to solve combinatorial linear programs
    • Tardos, E. (1986). A strongly polynomial algorithm to solve combinatorial linear programs. Operations Research, 34, 250-256.
    • (1986) Operations Research , vol.34 , pp. 250-256
    • Tardos, E.1
  • 76
    • 0041517242 scopus 로고
    • The minimum concave cost network flow problems with fixed number of sources and non-linear arc costs
    • Värbrand, P., Tuy, H., Ghannadan, S., & Migdalas, A. (1995). The minimum concave cost network flow problems with fixed number of sources and non-linear arc costs. Journal of Global Optimisation, 6, 135-151.
    • (1995) Journal of Global Optimisation , vol.6 , pp. 135-151
    • Värbrand, P.1    Tuy, H.2    Ghannadan, S.3    Migdalas, A.4
  • 77
    • 0006763479 scopus 로고    scopus 로고
    • A strongly polynomial algorithm for a concave production-transportation problem with a fixed number of non-linear variables
    • Värbrand, P., Tuy, H., Ghannadan, S., & Migdalas, A. (1996). A strongly polynomial algorithm for a concave production-transportation problem with a fixed number of non-linear variables. Mathematical Programming, 72, 229-258.
    • (1996) Mathematical Programming , vol.72 , pp. 229-258
    • Värbrand, P.1    Tuy, H.2    Ghannadan, S.3    Migdalas, A.4


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