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66
Steering Exact Penalty Methods for Nonlinear Programming
, 2007
"... This paper reviews, extends and analyzes a new class of penalty methods for nonlinear optimization. These methods adjust the penalty parameter dynamically; by controlling the degree of linear feasibility achieved at every iteration, they promote balanced progress toward optimality and feasibility. I ..."
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Cited by 11 (0 self)
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This paper reviews, extends and analyzes a new class of penalty methods for nonlinear optimization. These methods adjust the penalty parameter dynamically; by controlling the degree of linear feasibility achieved at every iteration, they promote balanced progress toward optimality and feasibility. In contrast with classical approaches, the choice of the penalty parameter ceases to be a heuristic and is determined, instead, by a subproblem with clearly defined objectives. The new penalty update strategy is presented in the context of sequential quadratic programming (SQP) and sequential linearquadratic programming (SLQP) methods that use trust regions to promote convergence. The paper concludes with a discussion of penalty parameters for merit functions used in line search methods.
Algorithms and software for convex mixed integer nonlinear programs, IMA Volumes
"... Abstract. This paper provides a survey of recent progress and software for solving convex mixed integer nonlinear programs (MINLP)s, where the objective and constraints are defined by convex functions and integrality restrictions are imposed on a subset of the decision variables. Convex MINLPs have ..."
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Cited by 10 (2 self)
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Abstract. This paper provides a survey of recent progress and software for solving convex mixed integer nonlinear programs (MINLP)s, where the objective and constraints are defined by convex functions and integrality restrictions are imposed on a subset of the decision variables. Convex MINLPs have received sustained attention in recent years. By exploiting analogies to wellknown techniques for solving mixed integer linear programs and incorporating these techniques into software, significant improvements have been made in the ability to solve these problems. Key words. Mixed Integer Nonlinear Programming; Branch and Bound; AMS(MOS) subject classifications.
The TOMLAB OPERA Toolbox for Linear and Discrete Optimization. Advanced Modeling and Optimization
, 1999
"... The Matlab toolbox OPERA TB is a set of Matlab m les, which solves basic linear and discrete optimization problems in operations research and mathematical programming. Included are routines for linear programming (LP), network programming (NP), integer programming (IP) and dynamic programming (DP). ..."
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Cited by 9 (8 self)
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The Matlab toolbox OPERA TB is a set of Matlab m les, which solves basic linear and discrete optimization problems in operations research and mathematical programming. Included are routines for linear programming (LP), network programming (NP), integer programming (IP) and dynamic programming (DP). OPERA TB, like the nonlinear programming toolbox NLPLIB TB, is a part of TOMLAB � an environment in Matlab for research and teaching in optimization. Linear programs are solved either by direct call to a solver routine or to a multisolver driver routine, or interactively, using the Graphical User Interface (GUI) or a menu system. From OPERA TB it is possible to call solvers in the Math Works Optimization Toolbox and, using a MEX le interface, generalpurpose solvers implemented in Fortran or C. The focus is on dense problems, but sparse linear programs may be solved using the commercial solver MINOS. Presently, OPERA TB implements about thirty algorithms and includes a set of test examples and demonstration les. This paper gives an overview of OPERA TB and presents test results for medium size LP problems. The tests show that the OPERA TB solver converges as fast as commercial Fortran solvers and is at least ve times faster than the simplex LP solver in the Optimization Toolbox 2.0andtwice as fast as the primaldual interiorpointLP solver in the same toolbox. Running the commercial Fortran solvers using MEX le interfaces gives a speedup factor of ve to thirty ve.
The TOMLAB NLPLIB Toolbox for Nonlinear Programming. Advanced Modeling and Optimization
, 1999
"... The paper presents the toolbox NLPLIB TB 1.0 (NonLinear Programming LIBrary) � a set of Matlab solvers, test problems, graphical and computational utilities for unconstrained and constrained optimization, quadratic programming, unconstrained and constrained nonlinear least squares, boxbounded globa ..."
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Cited by 9 (7 self)
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The paper presents the toolbox NLPLIB TB 1.0 (NonLinear Programming LIBrary) � a set of Matlab solvers, test problems, graphical and computational utilities for unconstrained and constrained optimization, quadratic programming, unconstrained and constrained nonlinear least squares, boxbounded global optimization, global mixedinteger nonlinear programming, and exponential sum model tting. NLPLIB TB, like the toolbox OPERA TB for linear and discrete optimization, is a part of TOMLAB � an environment in Matlab for research and teaching in optimization. TOMLAB currently solves small and medium size dense problems. Presently, NLPLIB TB implements more than 25 solver algorithms, and it is possible to call solvers in the Matlab Optimization Toolbox. MEX le interfaces are prepared for seven Fortran and C solvers, and others are easily added using the same type of interface routines. Currently, MEX le interfaces have beendeveloped for MINOS, NPSOL, NPOPT, NLSSOL, LPOPT, QPOPT and LSSOL. There are four ways to solve a problem: by a direct call to the solver routine or a call to amultisolver driver routine, or interactively, using the Graphical
Multihour Design of MultiHop Virtual Path based WideArea ATM Networks
 IN 15TH INTERNATIONAL TELETRAFFIC CONGRESS  ITC 15
, 1997
"... The cost efficient design of ATM networks is considered to be a challenging problem due to the heterogenity of services, the statistical muliplexing gain resulting from the resource sharing of variable bitrate (VBR) connections and the possibility of resource separation through virtual paths (VPs) ..."
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Cited by 8 (0 self)
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The cost efficient design of ATM networks is considered to be a challenging problem due to the heterogenity of services, the statistical muliplexing gain resulting from the resource sharing of variable bitrate (VBR) connections and the possibility of resource separation through virtual paths (VPs). Most proposals in literature are well suited for small problems only. For that before developing a new algorithm we take a look at large scale design techniques known from telephone network dimensioning. It turns out that the well known Unified Algorithm (UA) of G. Ash [1] is a good basis for an ATM network design method. So we extend and improve the UA in order to cope with the following multihour multiservice ATM network design problem: Find the minimum cost VP network structure on top of a given physical network and the design hour individual optimal VC routing sequences according to endtoend call blocking constraints. Beside transmission costs also virtual path/virtual channe...
Newton methods for largescale linear inequalityconstrained minimization
 SIAM Journal on Optimization
, 1997
"... Abstract. Newton methods of the linesearch type for largescale minimization subject to linear inequality constraints are discussed. The purpose of the paper is twofold: (i) to give an active–settype method with the ability to delete multiple constraints simultaneously and (ii) to give a relatively ..."
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Cited by 7 (0 self)
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Abstract. Newton methods of the linesearch type for largescale minimization subject to linear inequality constraints are discussed. The purpose of the paper is twofold: (i) to give an active–settype method with the ability to delete multiple constraints simultaneously and (ii) to give a relatively short general convergence proof for such a method. It is also discussed how multiple constraints can be added simultaneously. The approach is an extension of a previous work by the same authors for equalityconstrained problems. It is shown how the search directions can be computed without the need to compute the reduced Hessian of the objective function. The convergence analysis states that every limit point of a sequence of iterates satisfies the secondorder necessary optimality conditions. Key words. linear inequalityconstrained minimization, negative curvature, modified Newton method, symmetric indefinite factorization, largescale minimization, linesearch method
Assessing the Potential of Interior Methods for Nonlinear Optimization
, 2002
"... A series of numerical experiments with interior point (LOQO, KNITRO) and activeset sequential quadratic programming (SNOPT, filterSQP) codes are reported and analyzed. The tests were performed with small, mediumsize and moderately large problems, and are examined by problem classes. Detailed obser ..."
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Cited by 7 (1 self)
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A series of numerical experiments with interior point (LOQO, KNITRO) and activeset sequential quadratic programming (SNOPT, filterSQP) codes are reported and analyzed. The tests were performed with small, mediumsize and moderately large problems, and are examined by problem classes. Detailed observations on the performance of the codes, and several suggestions on how to improve them are presented. Overall, interior methods appear to be strong competitors of activeset SQP methods, but all codes show much room for improvement. 1
Optimal Decision Trees
 R.P.I. Math Report No. 214, Rensselaer Polytechnic Institute
, 1996
"... We propose an Extreme Point Tabu Search (EPTS) algorithm that constructs globally optimal decision trees for classification problems. Typically, decision tree algorithms are greedy. They optimize the misclassification error of each decision sequentially. Our nongreedy approach minimizes the misclas ..."
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Cited by 6 (2 self)
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We propose an Extreme Point Tabu Search (EPTS) algorithm that constructs globally optimal decision trees for classification problems. Typically, decision tree algorithms are greedy. They optimize the misclassification error of each decision sequentially. Our nongreedy approach minimizes the misclassification error of all the decisions in the tree concurrently. Using Global Tree Optimization (GTO), we can optimize existing decision trees. This capability can be used in classification and data mining applications to avoid overfitting, transfer knowledge, incorporate domain knowledge, and maintain existing decision trees. Our method works by fixing the structure of the decision tree and then representing it as a set of disjunctive linear inequalities. An optimization problem is constructed that minimizes the errors within the disjunctive linear inequalities. To reduce the misclassification error, a nonlinear error function is minimized over a polyhedral region. We show that it is suffici...
Interaction Between Real and Virtual Humans: Playing Checkers
 Proc. Eurographics Workshop on Virtual Environments
, 2000
"... . For some years, we have been able to integrate virtual humans into virtual environments. As the demand for Augmented Reality systems grows, so will the need for these synthetic humans to coexist and interact with humans who live in the real world. In this paper, we use the example of a checkers ..."
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Cited by 6 (2 self)
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. For some years, we have been able to integrate virtual humans into virtual environments. As the demand for Augmented Reality systems grows, so will the need for these synthetic humans to coexist and interact with humans who live in the real world. In this paper, we use the example of a checkers game between a real and a virtual human to demonstrate the integration of techniques required to achieve a realisticlooking interaction in realtime. We do not use cumbersome devices such as a magnetic motion capture system. Instead, we rely on purely imagebased techniques to address the registration issue, when the camera or the objects move, and to drive the virtual human's behavior. 1 Introduction Recent developments in Virtual Reality and Human Animation have led to the integration of Virtual Humans into synthetic environments. We can now interact with them and represent ourselves as avatars in the Virtual World [4]. Fast workstations make it feasible to animate them in realtime...
Treatment Planning for ImageGuided Robotic Radiosurgery
, 1997
"... . Radiosurgery is a noninvasive procedure that uses focused beams of radiation to destroy brain tumors. Treatment planning for radiosurgery involves determining a series of beam configurations that will destroy the tumor without damaging healthy tissue in the brain, particularly critical structures ..."
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Cited by 6 (2 self)
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. Radiosurgery is a noninvasive procedure that uses focused beams of radiation to destroy brain tumors. Treatment planning for radiosurgery involves determining a series of beam configurations that will destroy the tumor without damaging healthy tissue in the brain, particularly critical structures. A new imageguided robotic radiosurgical system has been developed at Stanford University in a joint project with Accuray, Inc. It has been in clinical use at Stanford since July, 1994, and thus far three patients have been treated with it. This system provides much more flexibility for treatment planning than do traditional radiosurgical systems. In order to take full advantage of this added flexibility, we have developed automatic methods for treatment planning. Our planner enables a surgeon to specify constraints interactively on the distribution of dose delivered and then to find a set of beam configurations that will satisfy these constraints. We provide a detailed description of our ...