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66
An InteriorPoint Algorithm For Nonconvex Nonlinear Programming
 COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
, 1997
"... The paper describes an interiorpoint algorithm for nonconvex nonlinear programming which is a direct extension of interiorpoint methods for linear and quadratic programming. Major modifications include a merit function and an altered search direction to ensure that a descent direction for the mer ..."
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Cited by 174 (14 self)
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The paper describes an interiorpoint algorithm for nonconvex nonlinear programming which is a direct extension of interiorpoint methods for linear and quadratic programming. Major modifications include a merit function and an altered search direction to ensure that a descent direction for the merit function is obtained. Preliminary numerical testing indicates that the method is robust. Further, numerical comparisons with MINOS and LANCELOT show that the method is efficient, and has the promise of greatly reducing solution times on at least some classes of models.
Interior methods for nonlinear optimization
 SIAM Review
, 2002
"... Abstract. Interior methods are an omnipresent, conspicuous feature of the constrained optimization landscape today, but it was not always so. Primarily in the form of barrier methods, interiorpoint techniques were popular during the 1960s for solving nonlinearly constrained problems. However, their ..."
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Cited by 89 (4 self)
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Abstract. Interior methods are an omnipresent, conspicuous feature of the constrained optimization landscape today, but it was not always so. Primarily in the form of barrier methods, interiorpoint techniques were popular during the 1960s for solving nonlinearly constrained problems. However, their use for linear programming was not even contemplated because of the total dominance of the simplex method. Vague but continuing anxiety about barrier methods eventually led to their abandonment in favor of newly emerging, apparently more efficient alternatives such as augmented Lagrangian and sequential quadratic programming methods. By the early 1980s, barrier methods were almost without exception regarded as a closed chapter in the history of optimization. This picture changed dramatically with Karmarkar’s widely publicized announcement in 1984 of a fast polynomialtime interior method for linear programming; in 1985, a formal connection was established between his method and classical barrier methods. Since then, interior methods have advanced so far, so fast, that their influence has transformed both the theory and practice of constrained optimization. This article provides a condensed, selective look at classical material and recent research about interior methods for nonlinearly constrained optimization.
A Globally Convergent PrimalDual InteriorPoint Filter Method for Nonlinear Programming
, 2002
"... In this paper, the filter technique of Fletcher and Leyffer (1997) is used to globalize the primaldual interiorpoint algorithm for nonlinear programming, avoiding the use of merit functions and the updating of penalty parameters. The new algorithm decomposes the primaldual step obtained from the p ..."
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Cited by 40 (4 self)
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In this paper, the filter technique of Fletcher and Leyffer (1997) is used to globalize the primaldual interiorpoint algorithm for nonlinear programming, avoiding the use of merit functions and the updating of penalty parameters. The new algorithm decomposes the primaldual step obtained from the perturbed firstorder necessary conditions into a normal and a tangential step, whose sizes are controlled by a trustregion type parameter. Each entry in the filter is a pair of coordinates: one resulting from feasibility and centrality, and associated with the normal step; the other resulting from optimality (complementarity and duality), and related with the tangential step. Global convergence to firstorder critical points is proved for the new primaldual interiorpoint filter algorithm.
Failure of global convergence for a class of interior point methods for nonlinear programming
 Mathematical Programming
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A PrimalDual InteriorPoint Method for Nonlinear Programming with Strong Global and Local Convergence Properties
 SIAM Journal on Optimization
, 2002
"... An exactpenaltyfunctionbased schemeinspired from an old idea due to Mayne and Polak (Math. Prog., vol. 11, 1976, pp. 6780)is proposed for extending to general smooth constrained optimization problems any given feasible interiorpoint method for inequality constrained problems. It is s ..."
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Cited by 31 (5 self)
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An exactpenaltyfunctionbased schemeinspired from an old idea due to Mayne and Polak (Math. Prog., vol. 11, 1976, pp. 6780)is proposed for extending to general smooth constrained optimization problems any given feasible interiorpoint method for inequality constrained problems. It is shown that the primaldual interiorpoint framework allows for a simpler penalty parameter update rule than that discussed and analyzed by the originators of the scheme in the context of first order methods of feasible direction. Strong global and local convergence results are proved under mild assumptions. In particular, (i) the proposed algorithm does not su#er a common pitfall # Department of Electrical and Computer Engineering and Institute for Systems Research, University of Maryland, College Park, MD 20742, USA + IBM T.J. Watson Research Center, Yorktown Heights, NY 10598, USA # Applied Physics Laboratory, Laurel, MD 20723, USA Alphatech, Arlington, VA 22203, USA recently pointed out by Wachter and Biegler; and (ii) the positive definiteness assumption on the Hessian estimate, made in the original version of the algorithm, is relaxed, allowing for the use of exact Hessian information, resulting in local quadratic convergence. Promising numerical results are reported.
A Computationally Efficient Feasible Sequential Quadratic Programming Algorithm
 SIAM Journal on Optimization
, 2001
"... . A sequential quadratic programming (SQP) algorithm generating feasible iterates is described and analyzed. What distinguishes this algorithm from previous feasible SQP algorithms proposed by various authors is a reduction in the amount of computation required to generate a new iterate while the pr ..."
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Cited by 28 (0 self)
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. A sequential quadratic programming (SQP) algorithm generating feasible iterates is described and analyzed. What distinguishes this algorithm from previous feasible SQP algorithms proposed by various authors is a reduction in the amount of computation required to generate a new iterate while the proposed scheme still enjoys the same global and fast local convergence properties. A preliminary implementation has been tested and some promising numerical results are reported. Key words. sequential quadratic programming, SQP, feasible iterates, feasible SQP, FSQP AMS subject classifications. 49M37, 65K05, 65K10, 90C30, 90C53 PII. S1052623498344562 1.
Advances in Simultaneous Strategies for Dynamic Process Optimization
 Optimization, Chemical Engineering Science
, 2001
"... Introduction Over the past decade, applications in dynamic simulation have increased signicantly in the process industries. These are driven by strong competitive markets faced by operating companies along with tighter specications on process performance and regulatory limits. Moreover, the develop ..."
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Cited by 23 (6 self)
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Introduction Over the past decade, applications in dynamic simulation have increased signicantly in the process industries. These are driven by strong competitive markets faced by operating companies along with tighter specications on process performance and regulatory limits. Moreover, the developmentofpowerful commercial modeling tools for dynamic simulation, such as ASPEN Custom # ####### ########################## #### ############### ################### 1 Modeler and gProms, has led to their introduction in industry alongside their widely used steady state counterparts. Dynamic optimization is the natural extension of these dynamic simulation tools because it automates many of the decisions required for engineering studies. Applications of dynamic simulation can be classied into oline and online tasks. Oline tasks include: # Design to avoid undesirable transients for chemical process
The InteriorPoint Revolution in Constrained Optimization
 HighPerformance Algorithms and Software in Nonlinear Optimization
, 1998
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The interiorpoint revolution in optimization: history, recent developments, and lasting consequences
 Bull. Amer. Math. Soc. (N.S
, 2005
"... Abstract. Interior methods are a pervasive feature of the optimization landscape today, but it was not always so. Although interiorpoint techniques, primarily in the form of barrier methods, were widely used during the 1960s for problems with nonlinear constraints, their use for the fundamental pro ..."
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Cited by 18 (1 self)
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Abstract. Interior methods are a pervasive feature of the optimization landscape today, but it was not always so. Although interiorpoint techniques, primarily in the form of barrier methods, were widely used during the 1960s for problems with nonlinear constraints, their use for the fundamental problem of linear programming was unthinkable because of the total dominance of the simplex method. During the 1970s, barrier methods were superseded, nearly to the point of oblivion, by newly emerging and seemingly more efficient alternatives such as augmented Lagrangian and sequential quadratic programming methods. By the early 1980s, barrier methods were almost universally regarded as a closed chapter in the history of optimization. This picture changed dramatically in 1984, when Narendra Karmarkar announced a fast polynomialtime interior method for linear programming; in 1985, a formal connection was established between his method and classical barrier methods. Since then, interior methods have continued to transform both the theory and practice of constrained optimization. We present a condensed,
Feasible Interior Methods Using Slacks for Nonlinear Optimization
 Computational Optimization and Applications
, 2002
"... A slackbased feasible interior point method is described which can be derived as a modification of infeasible methods. The modification is minor for most line search methods, but trust region methods require special attention. It is shown how the Cauchy point, which is often computed in trust regio ..."
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Cited by 16 (2 self)
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A slackbased feasible interior point method is described which can be derived as a modification of infeasible methods. The modification is minor for most line search methods, but trust region methods require special attention. It is shown how the Cauchy point, which is often computed in trust region methods, must be modified so that the feasible method is effective for problems containing both equality and inequality constraints. The relationship between slackbased methods and traditional feasible methods is discussed. Numerical results showing the relative performance of feasible versus infeasible interior point methods are presented.