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481
SNOPT: An SQP Algorithm For LargeScale Constrained Optimization
, 2002
"... Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems with general inequality constraints (linear and nonlinear). We assume that first deriv ..."
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Cited by 582 (23 self)
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Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems with general inequality constraints (linear and nonlinear). We assume that first derivatives are available, and that the constraint gradients are sparse. We discuss
Benchmarking Optimization Software with Performance Profiles
, 2001
"... We propose performance profiles  distribution functions for a performance metric  as a tool for benchmarking and comparing optimization software. We show that performance profiles combine the best features of other tools for performance evaluation. 1 Introduction The benchmarking of optimi ..."
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Cited by 380 (8 self)
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We propose performance profiles  distribution functions for a performance metric  as a tool for benchmarking and comparing optimization software. We show that performance profiles combine the best features of other tools for performance evaluation. 1 Introduction The benchmarking of optimization software has recently gained considerable visibility. Hans Mittlemann's [13] work on a variety of optimization software has frequently uncovered deficiencies in the software and has generally led to software improvements. Although Mittelmann's efforts have gained the most notice, other researchers have been concerned with the evaluation and performance of optimization codes. As recent examples, we cite [1, 2, 3, 4, 6, 12, 17]. The interpretation and analysis of the data generated by the benchmarking process are the main technical issues addressed in this paper. Most benchmarking efforts involve tables displaying the performance of each solver on each problem for a set of metrics such...
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 311 (21 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.
Optimization by Direct Search: New Perspectives on Some Classical and Modern Methods
 SIAM REVIEW VOL. 45, NO. 3, PP. 385–482
, 2003
"... Direct search methods are best known as unconstrained optimization techniques that do not explicitly use derivatives. Direct search methods were formally proposed and widely applied in the 1960s but fell out of favor with the mathematical optimization community by the early 1970s because they lacked ..."
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Cited by 222 (15 self)
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Direct search methods are best known as unconstrained optimization techniques that do not explicitly use derivatives. Direct search methods were formally proposed and widely applied in the 1960s but fell out of favor with the mathematical optimization community by the early 1970s because they lacked coherent mathematical analysis. Nonetheless, users remained loyal to these methods, most of which were easy to program, some of which were reliable. In the past fifteen years, these methods have seen a revival due, in part, to the appearance of mathematical analysis, as well as to interest in parallel and distributed computing. This review begins by briefly summarizing the history of direct search methods and considering the special properties of problems for which they are well suited. Our focus then turns to a broad class of methods for which we provide a unifying framework that lends itself to a variety of convergence results. The underlying principles allow generalization to handle bound constraints and linear constraints. We also discuss extensions to problems with nonlinear constraints.
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 221 (7 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
Complete search in continuous global optimization and constraint satisfaction
 ACTA NUMERICA 13
, 2004
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Optimal Spilling for CISC Machines with Few Registers
 In Proceedings of the ACM SIGPLAN 2001 conference on Programming language design and implementation
, 2000
"... Register allocation based on graph coloring performs poorly for machines with few registers, if each temporary is held either in machine registers or memory over its entire lifetime. With the exception of shortlived temporaries, most temporaries must spill  including long lived temporaries that a ..."
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Cited by 78 (1 self)
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Register allocation based on graph coloring performs poorly for machines with few registers, if each temporary is held either in machine registers or memory over its entire lifetime. With the exception of shortlived temporaries, most temporaries must spill  including long lived temporaries that are used within inner loops. Liverange splitting before or during register allocation helps to alleviate the problem but prior techniques are sometimes complex, make no guarantees about subsequent colorability and thus require further iterations of splitting, pay no attention to addressing modes, and make no claim to optimality. We formulate the register allocation problem for CISC architectures with few registers in two parts: an integer linear program that determines the optimal location to break up the implementation of a live range between registers and memory, and a register assignment phase that we guarantee to complete without further spill code insertion. Our linear programming model ...
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 67 (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.
Optimal Local Topology Knowledge for Energy Efficient Geographical Routing in Sensor Networks
, 2004
"... Since sensor networks can be composed of a very large number of nodes, the developed protocols for these networks must be scalable. Moreover, these protocols must be designed to prolong the battery lifetime of the nodes. Typical existing routing techniques for ad hoc networks are known not to scale ..."
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Cited by 60 (3 self)
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Since sensor networks can be composed of a very large number of nodes, the developed protocols for these networks must be scalable. Moreover, these protocols must be designed to prolong the battery lifetime of the nodes. Typical existing routing techniques for ad hoc networks are known not to scale well. On the other hand, the socalled geographical routing algorithms are known to be scalable but their energy efficiency has never been extensively and comparatively studied. For this reason, a novel analytical framework is introduced. In a geographical routing algorithm, the packets are forwarded by a node to its neighbor based on their respective positions. The proposed framework allows to analyze the relationship between the energy efficiency of the routing tasks and the extension of the range of the topology knowledge for each node. The leading forwarding rules for geographical routing are compared in this framework, and the energy efficiency of each of them is studied. Moreover Partial Topology Knowledge Forwarding, a new forwarding scheme, is introduced. A wider topology knowledge can improve the energy efficiency of the routing tasks but can increase the cost of topology information due to signaling packets that each node must transmit and receive to acquire this information, especially in networks with high mobility. The problem of determining the optimal Knowledge Range for each node to make energy efficient geographical routing decisions is tackled by Integer Linear Programming. It is demonstrated that the problem is intrinsically localized, i.e., a limited knowledge of the topology is sufficient to take energy efficient forwarding decisions, and that the proposed forwarding scheme outperforms the others in typical application scenarios. For online solution of th...