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362
Snopt: An SQP Algorithm For LargeScale Constrained Optimization
, 1997
"... 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 332 (18 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.
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 246 (7 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 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.
Semisupervised support vector machines
 Advances in Neural Information Processing Systems
, 1998
"... We introduce a semisupervised support vector machine (S 3 VM) method. Given a training set of labeled data and a working set of unlabeled data, S 3 VM constructs a support vector machine using both the training and working sets. We use S 3 VM to solve the transduction problem using overall risk min ..."
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Cited by 174 (7 self)
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We introduce a semisupervised support vector machine (S 3 VM) method. Given a training set of labeled data and a working set of unlabeled data, S 3 VM constructs a support vector machine using both the training and working sets. We use S 3 VM to solve the transduction problem using overall risk minimization (ORM) posed by Vapnik. 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 S 3 VM model that minimizes both the misclassification error and the function capacity based on all the available data. We show how the S 3 VM model for 1norm linear support vector machines can be converted to a mixedinteger program and then solved exactly using integer programming. Results of S 3 VM and the standard 1norm support vector machine approach are compared on eleven 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, S 3 VM either improved or showed no significant difference in generalization compared to the traditional approach.
Optimization by direct search: New perspectives on some classical and modern methods
 SIAM Review
, 2003
"... Abstract. 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 t ..."
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Cited by 123 (13 self)
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Abstract. 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.
Complete search in continuous global optimization and constraint satisfaction, Acta Numerica 13
, 2004
"... A chapter for ..."
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 62 (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 ...
LOCALIZER  A Modeling Language for Local Search
 INFORMS JOURNAL OF COMPUTING
, 1997
"... Local search is a traditional technique to solve combinatorial search problems which has raised much interest in recent years. The design and implementation of local search algorithms is not an easy task in general and may require considerable experimentation and programming effort. However, contrar ..."
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Cited by 50 (7 self)
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Local search is a traditional technique to solve combinatorial search problems which has raised much interest in recent years. The design and implementation of local search algorithms is not an easy task in general and may require considerable experimentation and programming effort. However, contrary to global search, little support is available to assist the design and implementation of local search algorithms. This paper is an attempt to support the implementation of local search. It presents the preliminary design of Localizer, a modeling language which makes it possible to express local search algorithms in a notation close to their informal descriptions in scientific papers. Experimental results on our first implementation show the feasibility of the approach.
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 49 (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.
Test Scheduling for CoreBased Systems Using MixedInteger Linear Programming
, 2000
"... We present optimal solutions to the test scheduling problem for corebased systems. Given a set of tasks (test sets for the cores), a set of test resources (e.g., test buses, BIST hardware) and a test access architecture, we determine start times for the tasks such that the total test application ti ..."
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Cited by 46 (8 self)
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We present optimal solutions to the test scheduling problem for corebased systems. Given a set of tasks (test sets for the cores), a set of test resources (e.g., test buses, BIST hardware) and a test access architecture, we determine start times for the tasks such that the total test application time is minimized. We show that the test scheduling decision problem is equivalent to theprocessor open shop scheduling problem and is therefore NPcomplete. However, a commonly encountered instance of this problem ( =2) can be solved in polynomial time. For the general case ( 2), we present a mixedinteger linear programming (MILP) model for optimal scheduling and apply it to a representative corebased system using an MILP solver available in the public domain. We also extend the MILP model to allow optimal test set selection from a set of alternatives. Finally, we present an efficient heuristic algorithm for handling larger systems for which the MILP model may be infeasible. Index Ter...