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QPECgen, a MATLAB generator for mathematical programs with quadratic objectives and affine variational inequality constraints
"... . We describe a technique for generating a special class, called QPEC, of mathematical programs with equilibrium constraints, MPEC. A QPEC is a quadratic MPEC, that is an optimization problem whose objective function is quadratic, firstlevel constraints are linear, and secondlevel (equilibrium) co ..."
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Cited by 20 (5 self)
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. We describe a technique for generating a special class, called QPEC, of mathematical programs with equilibrium constraints, MPEC. A QPEC is a quadratic MPEC, that is an optimization problem whose objective function is quadratic, firstlevel constraints are linear, and secondlevel (equilibrium) constraints are given by a parametric affine variational inequality or one of its specialisations. The generator, written in MATLAB, allows the user to control different properties of the QPEC and its solution. Options include the proportion of degenerate constraints in both the first and second level, illconditioning, convexity of the objective, monotonicity and symmetry of the secondlevel problem, and so on. We believe these properties may substantially effect efficiency of existing methods for MPEC, and illustrate this numerically by applying several methods to generator test problems. Documentation and relevant codes can be found by visiting http://www.maths.mu.OZ.AU/~danny/qpecgendoc.h...
Benchmarking Global Optimization and Constraint Satisfaction Codes
 Global Optimization and Constraint Satisfaction, First International Workshop on Global Constraint Optimization and Constraint Satisfaction, COCOS 2002, LNCS2861
, 2003
"... A benchmarking suite describing over 1000 optimization problems and constraint satisfaction problems covering problems from dierent traditions is described, annotated with best known solutions, and accompanied by recommended benchmarking protocols for comparing test results. ..."
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Cited by 20 (3 self)
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A benchmarking suite describing over 1000 optimization problems and constraint satisfaction problems covering problems from dierent traditions is described, annotated with best known solutions, and accompanied by recommended benchmarking protocols for comparing test results.
Geometry in Learning
 In Geometry at Work
, 1997
"... One of the fundamental problems in learning is identifying members of two different classes. For example, to diagnose cancer, one must learn to discriminate between benign and malignant tumors. Through examination of tumors with previously determined diagnosis, one learns some function for distingui ..."
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Cited by 19 (6 self)
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One of the fundamental problems in learning is identifying members of two different classes. For example, to diagnose cancer, one must learn to discriminate between benign and malignant tumors. Through examination of tumors with previously determined diagnosis, one learns some function for distinguishing the benign and malignant tumors. Then the acquired knowledge is used to diagnose new tumors. The perceptron is a simple biologically inspired model for this twoclass learning problem. The perceptron is trained or constructed using examples from the two classes. Then the perceptron is used to classify new examples. We describe geometrically what a perceptron is capable of learning. Using duality, we develop a framework for investigating different methods of training a perceptron. Depending on how we define the "best" perceptron, different minimization problems are developed for training the perceptron. The effectiveness of these methods is evaluated empirically on four practical applic...
InexactRestoration Algorithm for Constrained Optimization
 Journal of Optimization Theory and Applications
, 1999
"... We introduce a new model algorithm for solving nonlinear programming problems. No slack variables are introduced for dealing with inequality constraints. Each iteration of the method proceeds in two phases. In the first phase, feasibility of the current iterate is improved and in second phase the ob ..."
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Cited by 19 (6 self)
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We introduce a new model algorithm for solving nonlinear programming problems. No slack variables are introduced for dealing with inequality constraints. Each iteration of the method proceeds in two phases. In the first phase, feasibility of the current iterate is improved and in second phase the objective function value is reduced in an approximate feasible set. The point that results from the second phase is compared with the current point using a nonsmooth merit function that combines feasibility and optimality. This merit function includes a penalty parameter that changes between different iterations. A suitable updating procedure for this penalty parameter is included by means of which it can be increased or decreased along different iterations. The conditions for feasibility improvement at the first phase and for optimality improvement at the second phase are mild, and largescale implementations of the resulting method are possible. We prove that under suitable conditions, that ...
A Simple and Efficient Procedure for Polyhedral Assembly Partitioning under Infinitesimal Motions
, 1995
"... We study the following problem: Given a collection A of polyhedral parts in 3D, determine whether there exists a subset S of the parts that can be moved as a rigid body by an infinitesimal translation and rotation, without colliding with the rest of the parts, A n S. A negative result implies that ..."
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Cited by 16 (4 self)
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We study the following problem: Given a collection A of polyhedral parts in 3D, determine whether there exists a subset S of the parts that can be moved as a rigid body by an infinitesimal translation and rotation, without colliding with the rest of the parts, A n S. A negative result implies that the object whose constituent parts are the collection A cannot be taken apart with two hands. A positive result, together with the list of movable parts in S and a direction of motion for S, can be used by an assembly sequence planner. This problem has attracted considerable attention within and outside the robotics community. We devise an efficient algorithm to solve this problem. Our solution is based on the ability to focus on selected portions of the tangent space of rigid motions and efficiently access these portions. The algorithm is complete (in the sense that it is guaranteed to find a solution if one exists) , simple, and improves significantly over the best previously known soluti...
CARABEAMER: A Treatment Planner for a Robotic Radiosurgical System with General Kinematics
 Medical Image Analysis
, 1998
"... : Stereotactic radiosurgery is a minimally invasive procedure that uses a focused beam of radiation as an ablative instrument to destroy brain tumors. To deposit a high dose of radiation in a tumor, while reducing the dose to healthy tissue, a large number of beams are crossfired at the tumor from m ..."
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Cited by 14 (5 self)
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: Stereotactic radiosurgery is a minimally invasive procedure that uses a focused beam of radiation as an ablative instrument to destroy brain tumors. To deposit a high dose of radiation in a tumor, while reducing the dose to healthy tissue, a large number of beams are crossfired at the tumor from multiple directions. The treatment planning problem (also called the inverse dosimetry problem) is to compute a set of beams that produces a desired dose distribution. So far, its investigation has focused on the generation of isocenterbased treatments in which the beam axes intersect at a common point, the isocenter. However, this restriction limits the applicability of the treatments to tumors having simple shapes. This paper describes carabeamer, a new treatment planner for a radiosurgical system in which the radiation source can be arbitrarily positioned and oriented by a sixdegreeoffreedom manipulator. This planner uses randomized techniques to guess a promising initial set of beams....
The ABACUS System for BranchandCutandPrice Algorithms in Integer Programming and Combinatorial Optimization
, 1998
"... The development of new mathematical theory and its application in software systems for the solution of hard optimization problems have a long tradition in mathematical programming. In this tradition we implemented ABACUS, an objectoriented software framework for branchandcutandprice algorithms ..."
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Cited by 14 (0 self)
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The development of new mathematical theory and its application in software systems for the solution of hard optimization problems have a long tradition in mathematical programming. In this tradition we implemented ABACUS, an objectoriented software framework for branchandcutandprice algorithms for the solution of mixed integer and combinatorial optimization problems. This paper discusses some difficulties in the implementation of branchandcutandprice algorithms for combinatorial optimization problems and shows how they are managed by ABACUS.
The TOMLAB Graphical User Interface for Nonlinear Programming. Advanced Modeling and Optimization
 in MATLAB. Annals of Operations Research, Modeling Languages and Approaches: Submitted
, 1999
"... The paper presents a Graphical User Interface (GUI) for nonlinear programming in Matlab. The GUI gives easy access to all features in the NLPLIB TB (NonLinear Programming LIBrary Toolbox) � a set of Matlab solvers, test problems, graphical and computational utilities for unconstrained and constrain ..."
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Cited by 13 (9 self)
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The paper presents a Graphical User Interface (GUI) for nonlinear programming in Matlab. The GUI gives easy access to all features in the NLPLIB TB (NonLinear Programming LIBrary Toolbox) � 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. The GUI also runs the linear programming problems in the linear and discrete optimization toolbox OPERA TB. Both NLPLIB TB and OPERA TB are part of TOMLAB � an environment in Matlab for research and teaching in optimization. Presently, NLPLIB TB implements more than 25 solver algorithms, and it is possible to call solvers in the Math Works Optimization Toolbox. MEX le interfaces are developed for seven Fortran and C solvers, and others are easily added using the same type of interface routines. 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 User Interface or a menu system. The GUI may alsobe used as a preprocessor to generate Matlab code for standalone runs. Alargeset of standard test problems is implemented in TOMLAB. Furthermore, using MEX le interfaces, problems in the CUTE test problem data base and problems de ned in the AMPL modeling language can be solved.
Optimization Techniques for Solving Elliptic Control Problems with Control and State Constraints. Part 2: Distributed Control
 Comp. Optim. Applic
"... : Part 2 continues the study of optimization techniques for elliptic control problems subject to control and state constraints and is devoted to distributed control. Boundary conditions are of mixed Dirichlet and Neumann type. Necessary conditions of optimality are formally stated in form of a local ..."
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Cited by 13 (3 self)
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: Part 2 continues the study of optimization techniques for elliptic control problems subject to control and state constraints and is devoted to distributed control. Boundary conditions are of mixed Dirichlet and Neumann type. Necessary conditions of optimality are formally stated in form of a local Pontryagin minimum principle. By introducing suitable discretization schemes, the control problem is transcribed into a nonlinear programming problem. The problems are formulated as AMPL [13] scripts and several optimization codes are applied. In particular, it is shown that a recently developed interior point method is able to solve theses problems even for high discretizations. Several numerical examples with Dirichlet and Neumann boundary conditions are provided that illustrate the performance of the algorithm for dierent types of controls including bang{bang controls. The necessary conditions of optimality are checked numerically in the presence of active control and state constraints....
Numerical Optimal Control Of Parabolic PDEs Using DASOPT
, 1997
"... . This paper gives a preliminary description of DASOPT, a software system for the optimal control of processes described by timedependent partial differential equations (PDEs). DASOPT combines the use of efficient numerical methods for solving differentialalgebraic equations (DAEs) with a package ..."
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Cited by 11 (6 self)
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. This paper gives a preliminary description of DASOPT, a software system for the optimal control of processes described by timedependent partial differential equations (PDEs). DASOPT combines the use of efficient numerical methods for solving differentialalgebraic equations (DAEs) with a package for largescale optimization based on sequential quadratic programming (SQP). DASOPT is intended for the computation of the optimal control of timedependent nonlinear systems of PDEs in two (and eventually three) spatial dimensions, including possible inequality constraints on the state variables. By the use of either finitedifference or finiteelement approximations to the spatial derivatives, the PDEs are converted into a large system of ODEs or DAEs. Special techniques are needed in order to solve this very large optimal control problem. The use of DASOPT is illustrated by its application to a nonlinear parabolic PDE boundary control problem in two spatial dimensions. Computational resu...