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95
Complete search in continuous global optimization and constraint satisfaction
 ACTA NUMERICA 13
, 2004
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Review of nonlinear mixedinteger and disjunctive programming techniques
 Optimization and Engineering
, 2002
"... This paper has as a major objective to present a unified overview and derivation of mixedinteger nonlinear programming (MINLP) techniques, Branch and Bound, OuterApproximation, Generalized Benders and Extended Cutting Plane methods, as applied to nonlinear discrete optimization problems that are ex ..."
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Cited by 84 (20 self)
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This paper has as a major objective to present a unified overview and derivation of mixedinteger nonlinear programming (MINLP) techniques, Branch and Bound, OuterApproximation, Generalized Benders and Extended Cutting Plane methods, as applied to nonlinear discrete optimization problems that are expressed in algebraic form. The solution of MINLP problems with convex functions is presented first, followed by a brief discussion on extensions for the nonconvex case. The solution of logic based representations, known as generalized disjunctive programs, is also described. Theoretical properties are presented, and numerical comparisons on a small process network problem.
Global Optimization of MixedInteger Nonlinear Programs: A Theoretical and Computational Study
 Mathematical Programming
, 2003
"... This work addresses the development of an efficient solution strategy for obtaining global optima of continuous, integer, and mixedinteger nonlinear programs. Towards this end, we develop novel relaxation schemes, range reduction tests, and branching strategies which we incorporate into the prototy ..."
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Cited by 71 (2 self)
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This work addresses the development of an efficient solution strategy for obtaining global optima of continuous, integer, and mixedinteger nonlinear programs. Towards this end, we develop novel relaxation schemes, range reduction tests, and branching strategies which we incorporate into the prototypical branchandbound algorithm. In the theoretical...
Interval Analysis on Directed Acyclic Graphs for Global Optimization
 J. Global Optimization
, 2004
"... A directed acyclic graph (DAG) representation of optimization problems represents each variable, each operation, and each constraint in the problem formulation by a node of the DAG, with edges representing the ow of the computation. ..."
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Cited by 45 (9 self)
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A directed acyclic graph (DAG) representation of optimization problems represents each variable, each operation, and each constraint in the problem formulation by a node of the DAG, with edges representing the ow of the computation.
MyExperience: A System for
 In Situ Tracing and Capturing of User Feedback on Mobile Phones. Proceedings of MobiSys 2007
, 2007
"... Abstract—With the protiferation of highspeed networks and networked services, prov~loning dfierentiated serviees to a d]verse user base with heterogeneous QoS requirements has beeome an important]problem. The traditional approach of resouree reservation and admiksion control provides both guarantee ..."
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Cited by 33 (9 self)
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Abstract—With the protiferation of highspeed networks and networked services, prov~loning dfierentiated serviees to a d]verse user base with heterogeneous QoS requirements has beeome an important]problem. The traditional approach of resouree reservation and admiksion control provides both guarantees and graded serviee+%however, at the cost of potentially underutilized resources and tindted sealabltity. In thu paper, we describe a WAN QoS prov~]on areMtecture that adaptively organizes beateffort bandwidth into stratified services with graded QoS properties such that the QoS needs of a diverse user base ean be effectively met. Our mdriteetu~BS (Stratitied Besteffort Service)pmmotes a simple user/shnple network reatkation where neither the user nor the network is burdened with complex comprrtationat responsibitities. SBS is scalablq efficient and adaptive, and it complements the guaranteed service archL teeturq sharing a common network substrate comprised of GPS routers. It is also a functional complemen ~ pmvi&oning QoS efficiently commensurate with user needs, albt4t at the cost of weaker pmteetilon. SBS is suited to noncooperative network envimnrnerrts where users belhave seltishly and resouree contention reaohrtion k m~rated by the principle of competitive interaction. A principat feature of SBS is the transformation of usercentric QoS prevision mechanisms—a defining characteristic of competitive interaction entaiting intimate user control of internal networlk rmoureesinto network.eentrie mechanisms while preserving the former’s resouree atloeation
Global minimization using an Augmented Lagrangian method with variable lowerlevel constraints
, 2007
"... A novel global optimization method based on an Augmented Lagrangian framework is introduced for continuous constrained nonlinear optimization problems. At each outer iteration k the method requires the εkglobal minimization of the Augmented Lagrangian with simple constraints, where εk → ε. Global c ..."
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Cited by 32 (1 self)
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A novel global optimization method based on an Augmented Lagrangian framework is introduced for continuous constrained nonlinear optimization problems. At each outer iteration k the method requires the εkglobal minimization of the Augmented Lagrangian with simple constraints, where εk → ε. Global convergence to an εglobal minimizer of the original problem is proved. The subproblems are solved using the αBB method. Numerical experiments are presented.
Computable representations for convex hulls of lowdimensional quadratic forms
, 2007
"... Let C be the convex hull of points { ( 1) ( 1 x x)T  x ∈ F ⊂ ℜ n}. Representing or approximating C is a fundamental problem for global optimization algorithms based on convex relaxations of products of variables. If n ≤ 4 and F is a simplex then C has a computable representation in terms of matric ..."
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Cited by 29 (11 self)
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Let C be the convex hull of points { ( 1) ( 1 x x)T  x ∈ F ⊂ ℜ n}. Representing or approximating C is a fundamental problem for global optimization algorithms based on convex relaxations of products of variables. If n ≤ 4 and F is a simplex then C has a computable representation in terms of matrices X that are doubly nonnegative (positive semidefinite and componentwise nonnegative). If n = 2 and F is a box, then C has a representation that combines semidefiniteness with constraints on product terms obtained from the reformulationlinearization technique (RLT). The simplex result generalizes known representations for the convex hull of {(x1, x2, x1x2)  x ∈ F} when F ⊂ ℜ 2 is a triangle, while the result for box constraints generalizes the wellknown fact that in this case the RLT constraints generate the convex hull of {(x1, x2, x1x2)  x ∈ F}. When n = 3 and F is a box, a representation for C can be obtained by utilizing the simplex result for n = 4 in conjunction with a triangulation of the 3cube.
Retrospective on Optimization
 25 TH YEAR ISSUE ON COMPUTERS AND CHEMICAL ENGINEERING
"... In this paper we provide a general classification of mathematical optimization problems, followed by a matrix of applications that shows the areas in which these problems have been typically applied in process systems engineering. We then provide a review of solution methods of the major types of op ..."
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Cited by 27 (1 self)
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In this paper we provide a general classification of mathematical optimization problems, followed by a matrix of applications that shows the areas in which these problems have been typically applied in process systems engineering. We then provide a review of solution methods of the major types of optimization problems for continuous and discrete variable optimization, particularly nonlinear and mixedinteger nonlinear programming. We also review their extensions to dynamic optimization and optimization under uncertainty. While these areas are still subject to significant research efforts, the emphasis in this paper is on major developments that have taken place over the last twenty five years.
Semidefinite programming versus the reformulationlinearization technique for nonconvex quadratically constrained quadratic programming
, 2007
"... We consider relaxations for nonconvex quadratically constrained quadratic programming (QCQP) based on semidefinite programming (SDP) and the reformulationlinearization technique (RLT). From a theoretical standpoint we show that the addition of a semidefiniteness condition removes a substantial por ..."
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Cited by 27 (5 self)
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We consider relaxations for nonconvex quadratically constrained quadratic programming (QCQP) based on semidefinite programming (SDP) and the reformulationlinearization technique (RLT). From a theoretical standpoint we show that the addition of a semidefiniteness condition removes a substantial portion of the feasible region corresponding to product terms in the RLT relaxation. On test problems we show that the use of SDP and RLT constraints together can produce bounds that are substantially better than either technique used alone. For highly symmetric problems we also consider the effect of symmetrybreaking based on tightened bounds on variables and/or order constraints. 1 1