Results 1  10
of
114
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 ..."
Abstract

Cited by 597 (24 self)
 Add to MetaCart
(Show Context)
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
An interiorpoint method for largescale l1regularized logistic regression
 Journal of Machine Learning Research
, 2007
"... Logistic regression with ℓ1 regularization has been proposed as a promising method for feature selection in classification problems. In this paper we describe an efficient interiorpoint method for solving largescale ℓ1regularized logistic regression problems. Small problems with up to a thousand ..."
Abstract

Cited by 290 (9 self)
 Add to MetaCart
(Show Context)
Logistic regression with ℓ1 regularization has been proposed as a promising method for feature selection in classification problems. In this paper we describe an efficient interiorpoint method for solving largescale ℓ1regularized logistic regression problems. Small problems with up to a thousand or so features and examples can be solved in seconds on a PC; medium sized problems, with tens of thousands of features and examples, can be solved in tens of seconds (assuming some sparsity in the data). A variation on the basic method, that uses a preconditioned conjugate gradient method to compute the search step, can solve very large problems, with a million features and examples (e.g., the 20 Newsgroups data set), in a few minutes, on a PC. Using warmstart techniques, a good approximation of the entire regularization path can be computed much more efficiently than by solving a family of problems independently.
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 ..."
Abstract

Cited by 188 (3 self)
 Add to MetaCart
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...
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 ..."
Abstract

Cited by 166 (4 self)
 Add to MetaCart
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
Computer Experiments
, 1996
"... Introduction Deterministic computer simulations of physical phenomena are becoming widely used in science and engineering. Computers are used to describe the flow of air over an airplane wing, combustion of gasses in a flame, behavior of a metal structure under stress, safety of a nuclear reactor, a ..."
Abstract

Cited by 118 (6 self)
 Add to MetaCart
Introduction Deterministic computer simulations of physical phenomena are becoming widely used in science and engineering. Computers are used to describe the flow of air over an airplane wing, combustion of gasses in a flame, behavior of a metal structure under stress, safety of a nuclear reactor, and so on. Some of the most widely used computer models, and the ones that lead us to work in this area, arise in the design of the semiconductors used in the computers themselves. A process simulator starts with a data structure representing an unprocessed piece of silicon and simulates the steps such as oxidation, etching and ion injection that produce a semiconductor device such as a transistor. A device simulator takes a description of such a device and simulates the flow of current through it under varying conditions to determine properties of the device such as its switching speed and the critical voltage at which it switches. A circuit simulator takes a list of devices and the
User's Guide For SNOPT 5.3: A Fortran Package For LargeScale Nonlinear Programming
, 1999
"... SNOPT is a generalpurpose system for solving optimization problems involving many variables and constraints. It minimizes a linear or nonlinear function subject to bounds on the variables and sparse linear or nonlinear constraints. It is suitable for largescale linear and quadratic programming ..."
Abstract

Cited by 96 (2 self)
 Add to MetaCart
(Show Context)
SNOPT is a generalpurpose system for solving optimization problems involving many variables and constraints. It minimizes a linear or nonlinear function subject to bounds on the variables and sparse linear or nonlinear constraints. It is suitable for largescale linear and quadratic programming and for linearly constrained optimization, as well as for general nonlinear programs. SNOPT finds solutions that are locally optimal , and ideally any nonlinear functions should be smooth and users should provide gradients. It is often more widely useful. For example, local optima are often global solutions, and discontinuities in the function gradients can often be tolerated if they are not too close to an optimum. Unknown gradients are estimated by finite differences. SNOPT uses a sequential quadratic programming (SQP) algorithm that obtains search directions from a sequence of quadratic programming subproblems. Each QP subproblem minimizes a quadratic model of a certain Lagrangian function subject to a linearization of the constraints. An augmented Lagrangian merit function is reduced along each search direction to ensure convergence from any starting point. SNOPT is most efficient if only some of the variables enter nonlinearly, or if the number of active constraints (including simple bounds) is nearly as large as the number of variables. SNOPT requires relatively few evaluations of the problem functions. Hence it is especially effective if the objective or constraint functions (and their gradients) are expensive to evaluate. The source code for SNOPT is suitable for any machine with a Fortran compiler. SNOPT may be called from a driver program (typically in Fortran, C or MATLAB). SNOPT can also be used as a standalone package, reading data in the MPS ...
Optimal Design of a CMOS OpAmp via Geometric Programming
"... We describe a new method for determining component values and transistor dimensions for CMOS operational amplifiers (opamps). We observe that a wide variety of design objectives and constraints have a special form, i.e., theyareposynomial functions of the design variables. As a result the amplifi ..."
Abstract

Cited by 85 (10 self)
 Add to MetaCart
(Show Context)
We describe a new method for determining component values and transistor dimensions for CMOS operational amplifiers (opamps). We observe that a wide variety of design objectives and constraints have a special form, i.e., theyareposynomial functions of the design variables. As a result the amplifier design problem can be expressed as a special form of optimization problem called geometric programming, for which very efficient global optimization methods have been developed. As a consequence we can efficiently determine globally optimal amplifier designs, or globally optimal tradeoffs among competing performance measures such as power, openloop gain, and bandwidth. Our method therefore yields completely automated synthesis of (globally) optimal CMOS amplifiers, directly from specifications. In this paper we apply this method to a specific, widely used operational amplifier architecture, showing in detail how to formulate the design problem as a geometric program. We compute globally optimal tradeoff 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 specifications for a variety of process conditions and parameters.
Finding Chaos in Noisy Systems
, 1991
"... In the past twenty years there has been much interest in the physical and biological sciences in nonlinear dynamical systems that appear to have random, unpredictable behavior. One important parameter of a dynamic system is the dominant Lyapunov exponent (LE). When the behavior of the system is comp ..."
Abstract

Cited by 72 (2 self)
 Add to MetaCart
In the past twenty years there has been much interest in the physical and biological sciences in nonlinear dynamical systems that appear to have random, unpredictable behavior. One important parameter of a dynamic system is the dominant Lyapunov exponent (LE). When the behavior of the system is compared for two similar initial conditions, this exponent is related to the rate at which the subsequent trajectories diverge. A bounded system with a positive LE is one operational definition of chaotic behavior. Most methods for determining the LE have assumed thousands of observations generated from carefully controlled physical experiments. Less attention has been given to estimating the LE for biological and economic systems that are subjected to random perturbations and observed over a limited amount of time. Using nonparametric regression techniques (Neural Networks and Thin Plate Splines) it is possible to consistently estimate the LE. The properties of these methods have been studied using simulated data and are applied to a biological time series: marten fur returns for the Hudson Bay Company (18201900). Based on a nonparametric analysis there is little evidence for lowdimensional chaos in these data. Although these methods appear to work well for systems perturbed by small amounts of noise, finding chaos in a system with a significant stochastic component may be difficult.
Development and Application of the Collaborative Optimization Architecture in a Multidisciplinary Design Environment
 Multidisciplinary Design Optimization: State of the Art
, 1996
"... Collaborative optimization is a design architecture applicable in any multidisciplinary analysis environment but specifically intended for largescale distributed analysis applications. In this approach, a complex problem is hierarchically decomposed along disciplinary boundaries into a number of su ..."
Abstract

Cited by 57 (3 self)
 Add to MetaCart
(Show Context)
Collaborative optimization is a design architecture applicable in any multidisciplinary analysis environment but specifically intended for largescale distributed analysis applications. In this approach, a complex problem is hierarchically decomposed along disciplinary boundaries into a number of subproblems which are brought into multidisciplinary agreement by a systemlevel coordination process. When applied to problems in a multidisciplinary design environment, this scheme has several advantages over traditional solution strategies. These advantageous features include reducing the amount of information transferred between disciplines, the removal of large iterationloops, allowing the use of different subspace optimizers among the various analysis groups, an analysis framework which is easily parallelized and can operate on heterogenous equipment, and a structural framework that is wellsuited for conventional disciplinary organizations. In this article, the collaborative architectu...