Results 1  10
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528
Quantum Error Correction Via Codes Over GF(4)
, 1997
"... The problem of finding quantumerrorcorrecting codes is transformed into the problem of finding additive codes over the field GF(4) which are selforthogonal with respect to a certain trace inner product. Many new codes and new bounds are presented, as well as a table of upper and lower bounds on s ..."
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Cited by 304 (18 self)
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The problem of finding quantumerrorcorrecting codes is transformed into the problem of finding additive codes over the field GF(4) which are selforthogonal with respect to a certain trace inner product. Many new codes and new bounds are presented, as well as a table of upper and lower bounds on such codes of length up to 30 qubits.
Nonlinear Programming without a penalty function
 Mathematical Programming
, 2000
"... In this paper the solution of nonlinear programming problems by a Sequential Quadratic Programming (SQP) trustregion algorithm is considered. The aim of the present work is to promote global convergence without the need to use a penalty function. Instead, a new concept of a "filter" is in ..."
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Cited by 252 (32 self)
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In this paper the solution of nonlinear programming problems by a Sequential Quadratic Programming (SQP) trustregion algorithm is considered. The aim of the present work is to promote global convergence without the need to use a penalty function. Instead, a new concept of a "filter" is introduced which allows a step to be accepted if it reduces either the objective function or the constraint violation function. Numerical tests on a wide range of test problems are very encouraging and the new algorithm compares favourably with LANCELOT and an implementation of Sl 1 QP.
Semisupervised support vector machines
 In Proc. NIPS
, 1998
"... We introduce a semisupervised support vector machine (S3yM) method. Given a training set of labeled data and a working set of unlabeled data, S3YM constructs a support vector machine using both the training and working sets. We use S3YM to solve the transduction problem using overall risk minimiza ..."
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Cited by 223 (6 self)
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We introduce a semisupervised support vector machine (S3yM) method. Given a training set of labeled data and a working set of unlabeled data, S3YM constructs a support vector machine using both the training and working sets. We use S3YM to solve the transduction problem using overall risk minimization (ORM) posed by Yapnik. The transduction problem is to estimate the value of a classification function at the given points in the working set. This contrasts with the standard inductive learning problem of estimating the classification function at all possible values and then using the fixed function to deduce the classes of the working set data. We propose a general S3YM model that minimizes both the misclassification error and the function capacity based on all the available data. We show how the S3YM model for Inorm linear support vector machines can be converted to a mixedinteger program and then solved exactly using integer programming. Results of S3YM and the standard Inorm support vector machine approach are compared on ten data sets. Our computational results support the statistical learning theory results showing that incorporating working data improves generalization when insufficient training information is available. In every case, S3YM either improved or showed no significant difference in generalization compared to the traditional approach. SemiSupervised Support Vector Machines 369 1
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 199 (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.
R.J.: Interiorpoint methods for nonconvex nonlinear programming: orderings and higherorder methods
 Mathematical Programming Ser. B
, 2000
"... Abstract. In this paper, we present the formulation and solution of optimization problems with complementarity constraints using an interiorpoint method for nonconvex nonlinear programming. We identify possible difficulties that could arise, such as unbounded faces of dual variables, linear depend ..."
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Cited by 117 (8 self)
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Abstract. In this paper, we present the formulation and solution of optimization problems with complementarity constraints using an interiorpoint method for nonconvex nonlinear programming. We identify possible difficulties that could arise, such as unbounded faces of dual variables, linear dependence of constraint gradients and initialization issues. We suggest remedies. We include encouraging numerical results on the MacMPEC test suite of problems.
The Empirical Behavior of Sampling Methods for Stochastic Programming
 Annals of Operations Research
, 2002
"... We investigate the quality of solutions obtained from sampleaverage approximations to twostage stochastic linear programs with recourse. We use a recently developed software tool executing on a computational grid to solve many large instances of these problems, allowing us to obtain highquality s ..."
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Cited by 115 (17 self)
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We investigate the quality of solutions obtained from sampleaverage approximations to twostage stochastic linear programs with recourse. We use a recently developed software tool executing on a computational grid to solve many large instances of these problems, allowing us to obtain highquality solutions and to verify optimality and nearoptimality of the computed solutions in various ways.
Wholeproteome prediction of protein function via graphtheoretic analysis of interaction maps
 BIOINFORMATICS, VOL. 21 SUPPL. 1 2005, PAGES I302–I310
, 2005
"... ..."
Mixed Integer Programming for MultiVehicle Path Planning
 In European Control Conference 2001
, 2001
"... This paper presents a new approach to fueloptimal path planning of multiple vehicles using a combination of linear and integer programming. The basic problem formulation is to have the vehicles move from an initial dynamic state to a final state without colliding with each other, while at the same ..."
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Cited by 90 (13 self)
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This paper presents a new approach to fueloptimal path planning of multiple vehicles using a combination of linear and integer programming. The basic problem formulation is to have the vehicles move from an initial dynamic state to a final state without colliding with each other, while at the same time avoiding other stationary and moving obstacles. It is shown that this problem can be rewritten as a linear program with mixed integer /linear constraints that account for the collision avoidance. A key benefit of this approach is that the path optimization can be readily solved using the CPLEX optimization software with an AMPL/Matlab interface. An example is worked out to show that the framework of mixed integer/linear programming is well suited for path planning and collision avoidance problems. Implementation issues are also considered. In particular, we compare receding horizon strategies with fixed arrival time approaches.
Approximating Optimal Spare Capacity Allocation by Successive Survivable Routing
 in Proc. IEEE INFOCOM
, 2001
"... Spare capacity allocation (SCA) is an important part of fault tolerant network design. In the spare capacity allocation problem one seeks to determine where to place spare capacity in the network and how much spare capacity must be allocated to guarantee seamless communications services survivable t ..."
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Cited by 69 (4 self)
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Spare capacity allocation (SCA) is an important part of fault tolerant network design. In the spare capacity allocation problem one seeks to determine where to place spare capacity in the network and how much spare capacity must be allocated to guarantee seamless communications services survivable to a set of failure scenarios (e.g., any single link failure) . Formulated as a multicommodity flow integer programming problem, SCA is known to be NPhard. In this paper, we provide a twopronged attack to approximate the optimal SCA solution: unravel the SCA structure and find an effective algorithm. First, a literature review on the SCA problem and its algorithms is provided. Second, a integer programming model for SCA is provided. Third, a simulated annealing algorithm using the above InP model is briefly introduced. Next, the structure of SCA is modeled by a matrix method. The perflow based backup path information are aggregated into a square matrix, called the spare provision matrix (SPM). The size of the SPM is the number of links. Using the SPM as the state information, a new adaptive algorithm is then developed to approximate the optimal SCA solution termed successive survivable routing (SSR). SSR routes linkdisjoint backup paths for each traffic flow one at a time. Each flow keeps updating its backup path according to the current network state as long as the backup path is not carrying any traffic. In this way, SSR can be implemented by shortest path algorithms using advertised state information with complexity of O##Link #. The analysis also shows that SSR is using a necessary condition of the optimal solution. The numerical results show that SSR has near optimal spare capacity allocation with substantial advantages in computation speed.
Coordinating Multiple Robots with Kinodynamic Constraints along Specified Paths
, 2005
"... This paper focuses on the collisionfree coordination of multiple robots with kinodynamic constraints along specified paths. We present an approach to generate continuous velocity profiles for multiple robots; these velocity profiles satisfy the dynamics constraints, avoid collisions, and minimize t ..."
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Cited by 68 (9 self)
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This paper focuses on the collisionfree coordination of multiple robots with kinodynamic constraints along specified paths. We present an approach to generate continuous velocity profiles for multiple robots; these velocity profiles satisfy the dynamics constraints, avoid collisions, and minimize the completion time. The approach, which combines techniques from optimal control and mathematical programming, consists of identifying collision segments along each robot's path, and then optimizing the robots' velocities along the collision and collisionfree segments. First, for each path segment for each robot, the minimum and maximum possible traversal times that satisfy the dynamics constraints are computed by solving the corresponding twopoint boundary value problems. The collision avoidance constraints for pairs of robots can then be combined to formulate a mixed integer nonlinear programming (MINLP) problem. Since this nonconvex MINLP model is difficult to solve, we describe two related mixed integer linear programming (MILP) formulations, which provide schedules that give lower and upper bounds on the optimum; the upper bound schedule is designed to provide continuous velocity trajectories that are feasible. The approach is illustrated with coordination of multiple robots, modeled as double integrators subject to velocity and acceleration constraints. An application to coordination of nonholonomic carlike robots is described, along with implementation results for 12 robots.