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373
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 232 (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 162 (27 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.
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 149 (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.
Interiorpoint methods for nonconvex nonlinear programming: Filter methods and merit functions
 Computational Optimization and Applications
, 2002
"... Abstract. In this paper, we present global and local convergence results for an interiorpoint method for nonlinear programming and analyze the computational performance of its implementation. The algorithm uses an ℓ1 penalty approach to relax all constraints, to provide regularization, and to bound ..."
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Cited by 86 (8 self)
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Abstract. In this paper, we present global and local convergence results for an interiorpoint method for nonlinear programming and analyze the computational performance of its implementation. The algorithm uses an ℓ1 penalty approach to relax all constraints, to provide regularization, and to bound the Lagrange multipliers. The penalty problems are solved using a simplified version of Chen and Goldfarb’s strictly feasible interiorpoint method [12]. The global convergence of the algorithm is proved under mild assumptions, and local analysis shows that it converges Qquadratically for a large class of problems. The proposed approach is the first to simultaneously have all of the following properties while solving a general nonconvex nonlinear programming problem: (1) the convergence analysis does not assume boundedness of dual iterates, (2) local convergence does not require the Linear Independence Constraint Qualification, (3) the solution of the penalty problem is shown to locally converge to optima that may not satisfy the KarushKuhnTucker conditions, and (4) the algorithm is applicable to mathematical programs with equilibrium constraints. Numerical testing on a set of general nonlinear programming problems, including degenerate problems and infeasible problems, confirm the theoretical results. We also provide comparisons to a highlyefficient nonlinear solver and thoroughly analyze the effects of enforcing theoretical convergence guarantees on the computational performance of the algorithm. 1.
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 72 (13 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 65 (12 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.
Statespace Planning by Integer Optimization
 In Proceedings of the Sixteenth National Conference on Artificial Intelligence
, 1999
"... This paper describes ILPPLAN, a framework for solving AI planning problems represented as integer linear programs. ILPPLAN extends the planning as satisfiability framework to handle plans with resources, action costs, and complex objective functions. We show that challenging planning problems can ..."
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Cited by 60 (0 self)
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This paper describes ILPPLAN, a framework for solving AI planning problems represented as integer linear programs. ILPPLAN extends the planning as satisfiability framework to handle plans with resources, action costs, and complex objective functions. We show that challenging planning problems can be effectively solved using both traditional branchand bound IP solvers and efficient new integer local search algorithms. ILPPLAN can find better quality solutions for a set of hard benchmark logistics planning problems than had been found by any earlier system. 1 Introduction In recent years the AI community witnessed the unexpected success of satisfiability testing as a method for solving statespace planning problems (Weld 1999). Kautz and Selman (1996) demonstrated that in certain computationally challenging domains, the approach of axiomatizing problems in propositional logic and solving them with general randomized SAT algorithms (SATPLAN) was competitive with or superior to the ...
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 51 (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 50 (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.