Phan Thien Thach


Department of Optimization and Control Theory
Research interests: Economic Model, Quasiconvex Duality

Office: Building A5, Room 210
Tel: +84 (0)4 37563474 /210


Professional Experiances


List Publications in MathSciNet



List of recent publications
1Phan Thien Thach, T. V. Thang, Problems with resource allocation constraints and optimization over the efficient set, Journal of Global Optimization, 58(2014), 481-495.
2Phan Thien Thach, T. V. Thang, Conjugate duality for vector-maximization problems,  Journal of Mathematical Analysis and Applications  376 (2011), 94 - 102.
3Phan Thien Thach, Duality equation and efficiency conditions in a vector optimization problem, Vietnam J. Math, 38 (2010), 1 -- 8.
4Phan Thien Thach, Quasi-convex duality for a mixed 0-1 variable problem and applications in production planning with set up costs, Acta Math. Vietnamica, 34 (2009), 245-256.
5Phan Thien Thach, Sensitivity analysis of an upper-linear-return consciously co-operative economy of a firm, Vietnam J. Math. 36 (2008),  337 - 352.
6Phan Thien Thach, Convexification by duality for a multiple Leontief technology production design problem, Vietnam J. Math. 35 (2007), 299 - 308.
7Hoang Tuy, Al-Khayyal Faiz, Phan Thien Thach, Monotonic optimization: branch and cut methods. Essays and surveys in global optimization, 39–78, GERAD 25th Anniv. Ser., 7, Springer, New York, 2005.
8Phan Thien Thach, Equilibrium prices and quasiconvex duality. In: Generalized convexity, generalized monotonicity and applications, 341 - 350, Nonconvex Optim. Appl. 77, Springer, New York, 2005.
9Hoang Tuy, Phan Thien Thach, Hiroshi Konno, Optimization of polynomial fractional functions. J. Global Optim. 29 (2004), 19 - 44.
10Phan Thien Thach, Dual preference in Leontief production problem and its extension, Vietnam J. Math. 32 (2004), 209 - 218.
11Rainer E. Burkard, Helidon Dollani, Phan Thien Thach, Linear approximations in a dynamic programming approach for the uncapacitated single-source minimum concave cost network flow problem in acyclic networks. J. Global Optim. 19 (2001), 121 - 139.
12H. Konno, Phan Thien Thach, Hoang Tuy, Optimization on low rank nonconvex structures. Nonconvex Optimization and its Applications, 15. Kluwer Academic Publishers, Dordrecht, 1997. xii+457 pp.
13Phan Thien Thach, Hiroshi Konno, On the degree and separability of nonconvexity and appl-ications to optimization problems. Math. Programming 77 (1997), 23 - 47.
14Phan Thien Thach, H. Konno, D.C. Representability of closed sets in reflexive Banach spaces and applications to optimization problems. J. Optim. Theory Appl. 91 (1996), 1 - 22.
15Phan Thien Thach, H. Konno, D. Yokota, Dual approach to minimization on the set of Pareto-optimal solutions. J. Optim. Theory Appl. 88 (1996), 689 - 707.
16Phan Thien Thach, Masakazu Kojima, A generalized convexity and variational inequality for quasi-convex minimization. SIAM J. Optim. 6 (1996), 212 - 226.
17Phan Thien Thach, Diewert-Crouzeix conjugation for general quasiconvex duality and applications. J. Optim. Theory Appl. 86 (1995), 719 - 743.
18Phan Thien Thach, Global optimality criterion and a duality with a zero gap in nonconvex optimization. SIAM J. Math. Anal. 24 (1993), 1537 - 1556.
19Phan Thien Thach, Hiroshi Konno, A generalized Dantzig-Wolfe decomposition principle for a class of nonconvex programming problems. Math. Programming 62 (1993), 239 - 260.
20Phan Thien Thach, A generalized duality and applications. J. Global Optim. 3 (1993), 311 - 324.
21Phan Thien Thach, D.C. sets, D.C. functions and nonlinear equations. Math. Programming 58 (1993), 415 - 428.
22Phan Thien Thach, A decomposition method using a pricing mechanism for min concave cost flow problems with a hierarchical structure. Math. Programming 53 (1992), 339 - 359.
23Phan Thien Thach, New partitioning method for a class of nonconvex optimization problems. Math. Oper. Research 17 (1992), 43 - 60.
24Phan Thien Thach, R. E. Burkard, W. Oettli, Mathematical programs with a two-dimen-sional reverse convex constraint. J. Global Optim. 1 (1991), 145 - 154.
25 Tanaka Takao, Phan Thien Thach, Suzuki Shigemichi, Two nonconvex minimization approaches for the problem of determining an economic ordering policy for jointly replenished items. J. Operations Research Society of Japan 34 (1991), 109 - 124.
26Phan Thien Thach, Quasiconjugates of functions, duality relationship between quasiconvex minimization under a reverse convex constraint and quasiconvex maximization under a convex constraint, and applications. J. Math. Anal. Appl. 159 (1991), 299 - 322.
27Phan Thien Thach, Convex minimization under Lipschitz constraints. J. Optimi. Theory Appl. 64 (1990), 595 - 614.
28Phan Thien Thach, Hoang Tuy, The relief indicator method for constrained global optimization. Naval Research Logistics 37 (1990), 473 - 497.
29Phan Thien Thach, A decomposition method for the min concave cost flow problem with a staircase structure. Japan J. Appl. Math. 7 (1990), 103 - 120.
30Phan Thien Thach, Hoang Tuy, Parametric approach to a class of nonconvex global optimization problems. Optimization 19 (1988), 3 - 11.
31Phan Thien Thach, Hoang Tuy, Parametric approach to a class of nonconvex global optimization problems. Optimization 19 (1987), 3 - 11.
32Phan Thien Thach, Hoang Tuy, Global optimization under Lipshitzian constraints. Japan J. Appl. Math. 4 (1987), 205 - 217.
33Phan Thien Thach, Convex programs with several additional reverse convex constraints. Acta Math. Vietnam. 10 (1985), 35 - 57.