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88
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 384 (22 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 269 (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...
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 174 (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.
CUTE: Constrained and unconstrained testing environment
, 1993
"... The purpose of this paper is to discuss the scope and functionality of a versatile environment for testing small and largescale nonlinear optimization algorithms. Although many of these facilities were originally produced by the authors in conjunction with the software package LANCELOT, we belie ..."
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Cited by 161 (3 self)
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The purpose of this paper is to discuss the scope and functionality of a versatile environment for testing small and largescale nonlinear optimization algorithms. Although many of these facilities were originally produced by the authors in conjunction with the software package LANCELOT, we believe that they will be useful in their own right and should be available to researchers for their development of optimization software. The tools are available by anonymous ftp from a number of sources and may, in many cases, be installed automatically. The scope of a major collection of test problems written in the standard input format (SIF) used by the LANCELOT software package is described. Recognising that most software was not written with the SIF in mind, we provide tools to assist in building an interface between this input format and other optimization packages. These tools already provide a link between the SIF and an number of existing packages, including MINOS and OSL. In ad...
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 96 (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.
Optimal design of a CMOS opamp via geometric programming
 IEEE Transactions on ComputerAided Design
, 2001
"... We describe a new method for determining component values and transistor dimensions for CMOS operational ampli ers (opamps). We observe that a wide variety of design objectives and constraints have a special form, i.e., they are posynomial functions of the design variables. As a result the ampli er ..."
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Cited by 66 (10 self)
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We describe a new method for determining component values and transistor dimensions for CMOS operational ampli ers (opamps). We observe that a wide variety of design objectives and constraints have a special form, i.e., they are posynomial functions of the design variables. As a result the ampli er design problem can be expressed as a special form of optimization problem called geometric programming, for which very e cient global optimization methods have been developed. As a consequence we can e ciently determine globally optimal ampli er designs, or globally optimal tradeo s among competing performance measures such aspower, openloop gain, and bandwidth. Our method therefore yields completely automated synthesis of (globally) optimal CMOS ampli ers, directly from speci cations. In this paper we apply this method to a speci c, widely used operational ampli er architecture, showing in detail how to formulate the design problem as a geometric program. We compute globally optimal tradeo curves relating performance measures such as power dissipation, unitygain bandwidth, and openloop gain. We show how the method can be used to synthesize robust designs, i.e., designs guaranteed to meet the speci cations for a
Multicategory Classification by Support Vector Machines
 Computational Optimizations and Applications
, 1999
"... We examine the problem of how to discriminate between objects of three or more classes. Specifically, we investigate how twoclass discrimination methods can be extended to the multiclass case. We show how the linear programming (LP) approaches based on the work of Mangasarian and quadratic programm ..."
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Cited by 65 (0 self)
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We examine the problem of how to discriminate between objects of three or more classes. Specifically, we investigate how twoclass discrimination methods can be extended to the multiclass case. We show how the linear programming (LP) approaches based on the work of Mangasarian and quadratic programming (QP) approaches based on Vapnik's Support Vector Machines (SVM) can be combined to yield two new approaches to the multiclass problem. In LP multiclass discrimination, a single linear program is used to construct a piecewise linear classification function. In our proposed multiclass SVM method, a single quadratic program is used to construct a piecewise nonlinear classification function. Each piece of this function can take the form of a polynomial, radial basis function, or even a neural network. For the k > 2 class problems, the SVM method as originally proposed required the construction of a twoclass SVM to separate each class from the remaining classes. Similarily, k twoclass linear programs can be used for the multiclass problem. We performed an empirical study of the original LP method, the proposed k LP method, the proposed single QP method and the original k QP methods. We discuss the advantages and disadvantages of each approach. 1 1
KNITRO: An integrated package for nonlinear optimization
 Large Scale Nonlinear Optimization, 35–59, 2006
, 2006
"... This paper describes Knitro 5.0, a Cpackage for nonlinear optimization that combines complementary approaches to nonlinear optimization to achieve robust performance over a wide range of application requirements. The package is designed for solving largescale, smooth nonlinear programming problems ..."
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Cited by 52 (3 self)
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This paper describes Knitro 5.0, a Cpackage for nonlinear optimization that combines complementary approaches to nonlinear optimization to achieve robust performance over a wide range of application requirements. The package is designed for solving largescale, smooth nonlinear programming problems, and it is also effective for the following special cases: unconstrained optimization, nonlinear systems of equations, least squares, and linear and quadratic programming. Various algorithmic options are available, including two interior methods and an activeset method. The package provides crossover techniques between algorithmic options as well as automatic selection of options and settings. 1
Optimal operation of multi reservoir systems: stateoftheart review
 J. Water Resour. Plann. Manag
, 2004
"... Abstract: With construction of new largescale water storage projects on the wane in the U.S. and other developed countries, attention must focus on improving the operational effectiveness and efficiency of existing reservoir systems for maximizing the beneficial uses of these projects. Optimal coor ..."
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Cited by 46 (0 self)
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Abstract: With construction of new largescale water storage projects on the wane in the U.S. and other developed countries, attention must focus on improving the operational effectiveness and efficiency of existing reservoir systems for maximizing the beneficial uses of these projects. Optimal coordination of the many facets of reservoir systems requires the assistance of computer modeling tools to provide information for rational management and operational decisions. The purpose of this review is to assess the stateoftheart in optimization of reservoir system management and operations and consider future directions for additional research and application. Optimization methods designed to prevail over the highdimensional, dynamic, nonlinear, and stochastic characteristics of reservoir systems are scrutinized, as well as extensions into multiobjective optimization. Application of heuristic programming methods using evolutionary and genetic algorithms are described, along with application of neural networks and fuzzy rulebased systems for inferring reservoir system operating rules.
A Comparison of Complete Global Optimization Solvers
"... Results are reported of testing a number of existing state of the art solvers for global constrained optimization and constraint satisfaction on a set of over 1000 test problems in up to 1000 variables. ..."
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Cited by 25 (4 self)
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Results are reported of testing a number of existing state of the art solvers for global constrained optimization and constraint satisfaction on a set of over 1000 test problems in up to 1000 variables.