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37
Complete search in continuous global optimization and constraint satisfaction
 ACTA NUMERICA 13
, 2004
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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 48 (10 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.
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 39 (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.
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 38 (10 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
Reformulations in Mathematical Programming: A Computational Approach
"... Summary. Mathematical programming is a language for describing optimization problems; it is based on parameters, decision variables, objective function(s) subject to various types of constraints. The present treatment is concerned with the case when objective(s) and constraints are algebraic mathema ..."
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Cited by 24 (19 self)
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Summary. Mathematical programming is a language for describing optimization problems; it is based on parameters, decision variables, objective function(s) subject to various types of constraints. The present treatment is concerned with the case when objective(s) and constraints are algebraic mathematical expressions of the parameters and decision variables, and therefore excludes optimization of blackbox functions. A reformulation of a mathematical program P is a mathematical program Q obtained from P via symbolic transformations applied to the sets of variables, objectives and constraints. We present a survey of existing reformulations interpreted along these lines, some example applications, and describe the implementation of a software framework for reformulation and optimization. 1
Nonconvex mixedinteger nonlinear programming: A survey
 Surveys in Operations Research and Management Science
, 2012
"... A wide range of problems arising in practical applications can be formulated as MixedInteger Nonlinear Programs (MINLPs). For the case in which the objective and constraint functions are convex, some quite effective exact and heuristic algorithms are available. When nonconvexities are present, how ..."
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Cited by 20 (0 self)
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A wide range of problems arising in practical applications can be formulated as MixedInteger Nonlinear Programs (MINLPs). For the case in which the objective and constraint functions are convex, some quite effective exact and heuristic algorithms are available. When nonconvexities are present, however, things become much more difficult, since then even the continuous relaxation is a global optimisation problem. We survey the literature on nonconvex MINLP, discussing applications, algorithms and software. Special attention is paid to the case in which the objective and constraint functions are quadratic. Key Words: mixedinteger nonlinear programming, global optimisation, quadratic programming, polynomial optimisation.
On convex relaxations for quadratically constrained quadratic programming
 Mathematical Programming (Series B
, 2012
"... We consider convex relaxations for the problem of minimizing a (possibly nonconvex) quadratic objective subject to linear and (possibly nonconvex) quadratic constraints. Let F denote the feasible region for the linear constraints. We first show that replacing the quadratic objective and constraint f ..."
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Cited by 13 (0 self)
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We consider convex relaxations for the problem of minimizing a (possibly nonconvex) quadratic objective subject to linear and (possibly nonconvex) quadratic constraints. Let F denote the feasible region for the linear constraints. We first show that replacing the quadratic objective and constraint functions with their convex lower envelopes on F is dominated by an alternative methodology based on convexifying the range of the quadratic form () () 1 1 T x x for x ∈ F. We next show that the use of “αBB” underestimators as computable estimates of convex lower envelopes is dominated by a relaxation of the convex hull of the quadratic form that imposes semidefiniteness and linear constraints on diagonal terms. Finally, we show that the use of a large class of “D.C. ” underestimators is dominated by a relaxation that combines semidefiniteness with RLT constraints.
Rigorous filtering using linear relaxations
, 2010
"... This paper presents rigorous filtering methods for continuous constraint satisfaction problems based on linear relaxations. Filtering or pruning stands for reducing the search space of constraint satisfaction problems. Discussed are old and new approaches for rigorously enclosing the solution set o ..."
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Cited by 5 (3 self)
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This paper presents rigorous filtering methods for continuous constraint satisfaction problems based on linear relaxations. Filtering or pruning stands for reducing the search space of constraint satisfaction problems. Discussed are old and new approaches for rigorously enclosing the solution set of linear systems of inequalities, as well as different methods for computing linear relaxations. This allows custom combinations of relaxation and filtering. Care is taken to ensure that all methods correctly account for rounding errors in the computations. Although most of the results apply more generally, strong emphasis is given to relaxing and filtering quadratic constraints, as implemented in the GloptLab environment, which internally exploits a quadratic structure. Demonstrative examples and tests comparing the different linear relaxation methods are also presented.
MINLP Solver Software
, 2010
"... In this article we will give a brief overview of the startoftheart on software for the solution of mixed integer nonlinear programs (MINLP). We establish several groupings with respect to various features and give concise individual descriptions for each solver. ..."
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Cited by 3 (0 self)
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In this article we will give a brief overview of the startoftheart on software for the solution of mixed integer nonlinear programs (MINLP). We establish several groupings with respect to various features and give concise individual descriptions for each solver.