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, Symmetric Duality for Homogeneous Multiple-Objective Problems, Journal of Optimization Theory and Applications, 188 (2021), pages 317–331, SCI-E, Scopus.
2Phan Thien Thach, T. V. Thang, Problems with resource allocation constraints and optimization over the efficient set, Journal of Global Optimization, 58(2014), 481-495, SCI(-E); Scopus.
3Phan Thien Thach, T. V. Thang, Conjugate duality for vector-maximization problems,  Journal of Mathematical Analysis and Applications  376 (2011), 94 - 102, SCI(-E); Scopus.
4Phan Thien Thach, Duality equation and efficiency conditions in a vector optimization problem, Vietnam Journal of Mathematics 38 (2010), 1 -- 8, Scopus.
5Phan 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.
6Phan Thien Thach, Sensitivity analysis of an upper-linear-return consciously co-operative economy of a firm, Vietnam J. Math. 36 (2008),  337 - 352.
7Phan Thien Thach, Convexification by duality for a multiple Leontief technology production design problem, Vietnam J. Math. 35 (2007), 299 - 308.
8Hoang Tuy, Phan Thien Thach, Al-Khayyal Faiz, Monotonic optimization: branch and cut methods. Essays and surveys in global optimization, 39–78, GERAD 25th Anniv. Ser., 7, Springer, New York, 2005.
9Phan Thien Thach, Equilibrium prices and quasiconvex duality. In: Generalized convexity, generalized monotonicity and applications, 341 - 350, Nonconvex Optim. Appl. 77, Springer, New York, 2005.
10Hoang Tuy, Phan Thien Thach, Hiroshi Konno, Optimization of polynomial fractional functions. J. Global Optim. 29 (2004), 19 - 44.
11Phan Thien Thach, Dual preference in Leontief production problem and its extension, Vietnam J. Math. 32 (2004), 209 - 218.
12Rainer 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.
13H. 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.
14Phan Thien Thach, Hiroshi Konno, On the degree and separability of nonconvexity and appl-ications to optimization problems. Math. Programming 77 (1997), 23 - 47.
15Phan 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.
16Phan 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.
17Phan Thien Thach, Masakazu Kojima, A generalized convexity and variational inequality for quasi-convex minimization. SIAM J. Optim. 6 (1996), 212 - 226.
18Phan Thien Thach, Diewert-Crouzeix conjugation for general quasiconvex duality and applications. J. Optim. Theory Appl. 86 (1995), 719 - 743.
19Phan Thien Thach, Global optimality criterion and a duality with a zero gap in nonconvex optimization. SIAM J. Math. Anal. 24 (1993), 1537 - 1556.
20Phan Thien Thach, Hiroshi Konno, A generalized Dantzig-Wolfe decomposition principle for a class of nonconvex programming problems. Math. Programming 62 (1993), 239 - 260.
21Phan Thien Thach, A generalized duality and applications. J. Global Optim. 3 (1993), 311 - 324.
22Phan Thien Thach, D.C. sets, D.C. functions and nonlinear equations. Math. Programming 58 (1993), 415 - 428.
23Phan 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.
24Phan Thien Thach, New partitioning method for a class of nonconvex optimization problems. Math. Oper. Research 17 (1992), 43 - 60.
25Phan Thien Thach, R. E. Burkard, W. Oettli, Mathematical programs with a two-dimen-sional reverse convex constraint. J. Global Optim. 1 (1991), 145 - 154.
26 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.
27Phan 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.
28Phan Thien Thach, Convex minimization under Lipschitz constraints. J. Optimi. Theory Appl. 64 (1990), 595 - 614.
29Phan Thien Thach, Hoang Tuy, The relief indicator method for constrained global optimization. Naval Research Logistics 37 (1990), 473 - 497.
30Phan Thien Thach, A decomposition method for the min concave cost flow problem with a staircase structure. Japan J. Appl. Math. 7 (1990), 103 - 120.
31Hoang Tuy, Phan Thien Thach, Parametric approach to a class of nonconvex global optimization problems. Optimization 19 (1988), 3 - 11.
32Hoang Tuy, Phan Thien Thach, Parametric approach to a class of nonconvex global optimization problems. Optimization 19 (1987), 3 - 11.
33Hoang Tuy, Phan Thien Thach, Global optimization under Lipshitzian constraints. Japan J. Appl. Math. 4 (1987), 205 - 217.
34Phan Thien Thach, Convex programs with several additional reverse convex constraints. Acta Math. Vietnam. 10 (1985), 35 - 57.