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61
Complete search in continuous global optimization and constraint satisfaction, Acta Numerica 13
, 2004
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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 21 (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.
REFORMULATIONS IN MATHEMATICAL PROGRAMMING: DEFINITIONS AND SYSTEMATICS
, 2008
"... A reformulation of a mathematical program is a formulation which shares some properties with, but is in some sense better than, the original program. Reformulations are important with respect to the choice and efficiency of the solution algorithms; furthermore, it is desirable that reformulations c ..."
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Cited by 19 (14 self)
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A reformulation of a mathematical program is a formulation which shares some properties with, but is in some sense better than, the original program. Reformulations are important with respect to the choice and efficiency of the solution algorithms; furthermore, it is desirable that reformulations can be carried out automatically. Reformulation techniques are very common in mathematical programming but interestingly they have never been studied under a common framework. This paper attempts to move some steps in this direction. We define a framework for storing and manipulating mathematical programming formulations, give several fundamental definitions categorizing reformulations in essentially four types (optreformulations, narrowings, relaxations and approximations). We establish some theoretical results and give reformulation examples for each type.
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 18 (13 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
A Linear Relaxation Technique for the Position Analysis of Multiloop Linkages
 IEEE TRANSACTIONS ON ROBOTICS
"... This paper presents a new method to isolate all configurations that a multiloop linkage can adopt. The problem is tackled by means of formulation and resolution techniques that fit particularly well together. The adopted formulation yields a system of simple equations (only containing linear, biline ..."
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Cited by 14 (13 self)
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This paper presents a new method to isolate all configurations that a multiloop linkage can adopt. The problem is tackled by means of formulation and resolution techniques that fit particularly well together. The adopted formulation yields a system of simple equations (only containing linear, bilinear, and quadratic monomials, and trivial trigonometric terms for the helical pair only) whose structure is later exploited by a branchandprune method based on linear relaxations. The method is general, as it can be applied to linkages with single or multiple loops with arbitrary topology, involving lower pairs of any kind, and complete, as all possible solutions get accurately bounded, irrespectively of whether the linkage is rigid or mobile.
Evolutionary Computation for Global Optimization of NonLinear Chemical Engineering Processes
 Proceedings of International Symposium on Process Systems Engineering and Control (ISPSEC’ 03)  For Productivity Enhancement through Design and Optimization, IITBombay, Mumbai, January 34, 2003, Paper No. FMA2
, 2003
"... Abstract: Differential Evolution (DE) is an evolutionary optimization technique, which is exceptionally simple, significantly faster & robust at numerical optimization and is more likely to find a function’s true global optimum. In the present study, DE has been used to solve the two nonlinear ..."
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Cited by 8 (3 self)
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Abstract: Differential Evolution (DE) is an evolutionary optimization technique, which is exceptionally simple, significantly faster & robust at numerical optimization and is more likely to find a function’s true global optimum. In the present study, DE has been used to solve the two nonlinear chemical engineering problems. Comparison is made with αBB algorithm (which is based on a branchandbound approach). The results indicate that performance of DE is better than the αBB algorithm.
LaGO  An object oriented library for solving MINLPs, submitted for publication
 in COCOS’02 Conference Proceedings
, 2003
"... Abstract. The paper describes a software package called LaGO for solving nonconvex mixed integer nonlinear programs (MINLPs). The main component of LaGO is a convex relaxation which is used for generating solution candidates and computing lower bounds of the optimal value. The relaxation is generate ..."
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Cited by 8 (3 self)
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Abstract. The paper describes a software package called LaGO for solving nonconvex mixed integer nonlinear programs (MINLPs). The main component of LaGO is a convex relaxation which is used for generating solution candidates and computing lower bounds of the optimal value. The relaxation is generated by reformulating the given MINLP as a blockseparable problem, and replacing nonconvex functions by convex underestimators. Results on medium size MINLPs are presented.
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 7 (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.
Optimal running and planning of a biomassbased energy production process
, 2008
"... We propose ..."