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29
Sequential Quadratic Programming
, 1995
"... this paper we examine the underlying ideas of the SQP method and the theory that establishes it as a framework from which effective algorithms can ..."
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Cited by 114 (2 self)
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this paper we examine the underlying ideas of the SQP method and the theory that establishes it as a framework from which effective algorithms can
A Global Convergence Theory for General TrustRegionBased Algorithms for Equality Constrained Optimization
 SIAM Journal on Optimization
, 1992
"... This work presents a global convergence theory for a broad class of trustregion algorithms for the smooth nonlinear progro.mmln S problem with equality constraints. The main result generalizes Powell's 1975 result for unconstrained trustregion algorithms. ..."
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Cited by 42 (10 self)
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This work presents a global convergence theory for a broad class of trustregion algorithms for the smooth nonlinear progro.mmln S problem with equality constraints. The main result generalizes Powell's 1975 result for unconstrained trustregion algorithms.
Primaldual Strategy for Constrained Optimal Control Problems
, 1997
"... . An algorithm for efficient solution of control constrained optimal control problems is proposed and analyzed. It is based on an active set strategy involving primal as well as dual variables. For discretized problems sufficient conditions for convergence in finitely many iterations are given. Nume ..."
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Cited by 39 (4 self)
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. An algorithm for efficient solution of control constrained optimal control problems is proposed and analyzed. It is based on an active set strategy involving primal as well as dual variables. For discretized problems sufficient conditions for convergence in finitely many iterations are given. Numerical examples are given and the role of strict complementarity condition is discussed. Keywords: Active Set, Augmented Lagrangian, Primaldual method, Optimal Control. AMS subject classification. 49J20, 49M29 1. Introduction and formulation of the problem. In the recent past significant advances have been made in solving efficiently nonlinear optimal control problems. Most of the proposed methods are based on variations of the sequential quadratic programming (SQP) technique, see for instance [HT, KeS, KuS, K, T] and the references given there. The SQPalgorithm is sequential and each of its iterations requires the solution of a quadratic minimization problem subject to linearized constr...
NearPerfectReconstruction PseudoQMF
 IEEE Trans. Signal Processing
, 1994
"... A novel approach to the design of Mchannel pseudoquadrature mirror filter (QMF) banks is presented. In this approach, the prototype filter is constrained to be a linearphase spectralfactor of a 2_1Ith band filter. As a result, the overall transfer function of the analysis/synthesis system is a d ..."
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Cited by 34 (1 self)
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A novel approach to the design of Mchannel pseudoquadrature mirror filter (QMF) banks is presented. In this approach, the prototype filter is constrained to be a linearphase spectralfactor of a 2_1Ith band filter. As a result, the overall transfer function of the analysis/synthesis system is a delay. Moreover, the aliasing cancellation {AC) constraint is derived such that all the significant aliasing terms are canceled. Consequently, the aliasing level at the output is comparable to the stopband attenuation of the prototype filter. In other words, the only error at the output of the analysis/synthesis system is the aliasing error which is at the level of stopband attenuation. Using this approazh, it is possible to design a pseudoQMF bank where the stopband attenuation of the analysis land thus synthesis) filters is on the order of100 dB. Moreover, the resulting reconstruction error is also on the order of100 riB. Several examples are included.
TOMLAB  An Environment for Solving Optimization Problems in MATLAB
 PROCEEDINGS FOR THE NORDIC MATLAB CONFERENCE '97
, 1997
"... TOMLAB is a general purpose, open and integrated MATLAB environment for solving optimization problems on UNIX and PC systems. TOMLAB has meny systems and driver routines for the most common optimization problems and more than 50 algorithms implemented in the toolbox NLPLIB and the toolbox OPERA. N ..."
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Cited by 14 (12 self)
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TOMLAB is a general purpose, open and integrated MATLAB environment for solving optimization problems on UNIX and PC systems. TOMLAB has meny systems and driver routines for the most common optimization problems and more than 50 algorithms implemented in the toolbox NLPLIB and the toolbox OPERA. NLPLIB TB 1.0 is a MATLAB toolbox for nonlinear programming and parameter estimation and OPERA TB 1.0 is a MATLAB toolbox for operational research, with emphasis on linear and discrete optimization. Of special interest in NLPLIB TB 1.0 are the algorithms for general and separable nonlinear least squares parameter estimation. TOMLAB is using MEXfile interfaces to call solvers written in C/C++ and FORTRAN. Currently MEXfile interfaces have been developed for the commercial solvers MINOS, NPSOL, NPOPT, NLSSOL, LPOPT, QPOPT and LSSOL. From TOMLAB it is also possible to call routines in the MathWorks Optimization Toolbox. Interfaces are available for the model language AMPL and the CUTE (Cons...
TOMLAB  A General Purpose, Open MATLAB Environment for Research and Teaching in Optimization
, 1998
"... TOMLAB is a general purpose, open and integrated MATLAB environment for research and teaching in optimization on UNIX and PC systems. The motivation for TOMLAB is to simplify research on practical optimization problems, giving easy access to all types of solvers; at the same time having full acce ..."
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Cited by 14 (13 self)
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TOMLAB is a general purpose, open and integrated MATLAB environment for research and teaching in optimization on UNIX and PC systems. The motivation for TOMLAB is to simplify research on practical optimization problems, giving easy access to all types of solvers; at the same time having full access to the power of MATLAB. By using a simple, but general input format, combined with the ability in MATLAB to evaluate string expressions, it is possible to run internal TOMLAB solvers, MATLAB Optimization Toolbox and commercial solvers written in FORTRAN or C/C++ using MEXfile interfaces. Currently MEXfile interfaces have been developed for MINOS, NPSOL, NPOPT, NLSSOL, LPOPT, QPOPT and LSSOL. TOMLAB may either be used totally parameter driven or menu driven. The basic principles will be discussed. The menu system makes it suitable for teaching. Many standard test problems are included. More test problems are easily added. There are many example and demonstration files. Iterati...
The TOMLAB NLPLIB Toolbox for Nonlinear Programming. Advanced Modeling and Optimization
, 1999
"... The paper presents the toolbox NLPLIB TB 1.0 (NonLinear Programming LIBrary) � a set of Matlab solvers, test problems, graphical and computational utilities for unconstrained and constrained optimization, quadratic programming, unconstrained and constrained nonlinear least squares, boxbounded globa ..."
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Cited by 9 (7 self)
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The paper presents the toolbox NLPLIB TB 1.0 (NonLinear Programming LIBrary) � a set of Matlab solvers, test problems, graphical and computational utilities for unconstrained and constrained optimization, quadratic programming, unconstrained and constrained nonlinear least squares, boxbounded global optimization, global mixedinteger nonlinear programming, and exponential sum model tting. NLPLIB TB, like the toolbox OPERA TB for linear and discrete optimization, is a part of TOMLAB � an environment in Matlab for research and teaching in optimization. TOMLAB currently solves small and medium size dense problems. Presently, NLPLIB TB implements more than 25 solver algorithms, and it is possible to call solvers in the Matlab Optimization Toolbox. MEX le interfaces are prepared for seven Fortran and C solvers, and others are easily added using the same type of interface routines. Currently, MEX le interfaces have beendeveloped for MINOS, NPSOL, NPOPT, NLSSOL, LPOPT, QPOPT and LSSOL. There are four ways to solve a problem: by a direct call to the solver routine or a call to amultisolver driver routine, or interactively, using the Graphical
A Merit Function for Inequality Constrained Nonlinear Programming Problems
 Internal Report 4702, National Institute of Standards and Technology
, 1993
"... We consider the use of the sequential quadratic programming (SQP) technique for solving the inequality constrained minimization problem min x f(x) subject to: g i (x) 0; i = 1; : : : ; m: SQP methods require the use of an auxiliary function, called a merit function or linesearch function, for asse ..."
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Cited by 5 (4 self)
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We consider the use of the sequential quadratic programming (SQP) technique for solving the inequality constrained minimization problem min x f(x) subject to: g i (x) 0; i = 1; : : : ; m: SQP methods require the use of an auxiliary function, called a merit function or linesearch function, for assessing the steps that are generated. We derive a merit function by adding slack variables to create an equality constrained problem and then using the merit function developed earlier by the authors for the equality constrained case. We stress that we do not solve the slack variable problem, but only use it to construct the merit function. The resulting function is simplified in a certain way that leads to an effective procedure for updating the squares of the slack variables. A globally convergent algorithm, based on this merit function, is suggested, and is demonstrated to be effective in practice. Contribution of the National Institute of Standards and Technology and not subject to copyr...
The TOMLAB Optimization Environment in Matlab
, 1999
"... TOMLAB is a general purpose, open and integrated Matlab development environment for research and teaching in optimization on Unix and PC systems. One motivation for TOMLAB is to simplify research on practical optimization problems, giving easy access to all types of solvers; at the same time having ..."
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Cited by 5 (0 self)
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TOMLAB is a general purpose, open and integrated Matlab development environment for research and teaching in optimization on Unix and PC systems. One motivation for TOMLAB is to simplify research on practical optimization problems, giving easy access to all types of solvers; at the same time having full access to the power of Matlab. The design principle is: define your problem once, optimize using any suitable solver. In this paper we discuss the design and contents of TOMLAB, as well as some applications where TOMLAB has been successfully applied. TOMLAB is based on NLPLIB TB, a Matlab toolbox for nonlinear programming and parameter estimation, and OPERA TB 1.0, a Matlab toolbox for linear and discrete optimization. More than 65 different algorithms and graphical utilities are implemented. It is possible to call solvers in the Matlab Optimization Toolbox and generalpurpose solvers implemented in Fortran or C using a MEXfile interface. Currently, MEXfile interfaces have been developed for
A Robust Algorithm for Optimization With General Equality and Inequality Constraints
 of Unkown Multipath Channels Based on Block Precoding and Transmit Diversity,” in Asilomar Conference on Signals, Systems, and Computers
"... An algorithm for general nonlinearly constrained optimization is presented, which solves an unconstrained piecewise quadratic subproblem and a quadratic programming subproblem at each iterate. The algorithm is robust since it can circumvent the difficulties associated with the possible inconsistency ..."
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Cited by 5 (4 self)
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An algorithm for general nonlinearly constrained optimization is presented, which solves an unconstrained piecewise quadratic subproblem and a quadratic programming subproblem at each iterate. The algorithm is robust since it can circumvent the difficulties associated with the possible inconsistency of QP subproblem of the original SQP method. Moreover, the algorithm can converge to a point which satisfies a certain firstorder necessary optimality condition even when the original problem is itself infeasible, which is a feature of Burke and Han's methods(1989). Unlike Burke and Han's methods(1989), however, we do not introduce additional bound constraints. The algorithm solves the same subproblems as HanPowell SQP algorithm at feasible points of the original problem. Under certain assumptions, it is shown that the algorithm coincide with the HanPowell method when the iterates are sufficiently close to the solution. Some global convergence results are proved and local superlinear co...