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LargeScale Optimization of Eigenvalues
 SIAM J. Optimization
, 1991
"... Optimization problems involving eigenvalues arise in many applications. Let x be a vector of real parameters and let A(x) be a continuously differentiable symmetric matrix function of x. We consider a particular problem which occurs frequently: the minimization of the maximum eigenvalue of A(x), ..."
Abstract

Cited by 78 (3 self)
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Optimization problems involving eigenvalues arise in many applications. Let x be a vector of real parameters and let A(x) be a continuously differentiable symmetric matrix function of x. We consider a particular problem which occurs frequently: the minimization of the maximum eigenvalue of A(x), subject to linear constraints and bounds on x. The eigenvalues of A(x) are not differentiable at points x where they coalesce, so the optimization problem is said to be nonsmooth. Furthermore, it is typically the case that the optimization objective tends to make eigenvalues coalesce at a solution point. There are three main purposes of the paper. The first is to present a clear and selfcontained derivation of the Clarke generalized gradient of the max eigenvalue function in terms of a "dual matrix". The second purpose is to describe a new algorithm, based on the ideas of a previous paper by the author (SIAM J. Matrix Anal. Appl. 9 (1988) 256268), which is suitable for solving l...
A Sqp Method For General Nonlinear Programs Using Only Equality Constrained Subproblems
 MATHEMATICAL PROGRAMMING
, 1993
"... In this paper we describe a new version of a sequential equality constrained quadratic programming method for general nonlinear programs with mixed equality and inequality constraints. Compared with an older version [34] it is much simpler to implement and allows any kind of changes of the working s ..."
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Cited by 48 (2 self)
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In this paper we describe a new version of a sequential equality constrained quadratic programming method for general nonlinear programs with mixed equality and inequality constraints. Compared with an older version [34] it is much simpler to implement and allows any kind of changes of the working set in every step. Our method relies on a strong regularity condition. As far as it is applicable the new approach is superior to conventional SQPmethods, as demonstrated by extensive numerical tests.
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 39 (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
Partially Reduced SQP Methods For LargeScale Nonlinear Optimization Problems
, 1997
"... this paper we investigate more closely the structures of two application examples which can be considered representative for the rather wide class of largescale optimization problems in so far as they stem from discretizations: ..."
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Cited by 5 (0 self)
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this paper we investigate more closely the structures of two application examples which can be considered representative for the rather wide class of largescale optimization problems in so far as they stem from discretizations:
ComputerAided Motion Planning For Satellite Mounted Robots
, 1998
"... In space based robotics, one of the most important problems is the disturbance to the satellite attitude and to the satellite microgravity environment caused by satellite mounted robot operation. This paper reports on computeraided motion planning strategies to overcome this problem. Point to point ..."
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Cited by 2 (1 self)
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In space based robotics, one of the most important problems is the disturbance to the satellite attitude and to the satellite microgravity environment caused by satellite mounted robot operation. This paper reports on computeraided motion planning strategies to overcome this problem. Point to point motion designs are generated which not only connect prescribed start and end points of the robot motion, but also simultaneously return the satellite to its original attitude. Theoretical characterizations of some of those motion designs are presented, as well as numerical results. The computation time required to produce such motion designs is 1 or 2 minutes on a workstation. Thus, it can be practical to use these motion plans in space. Introduction Satellite mounted robots can aid in the automated assembly of large structures in space and sometimes eliminate the need for extravehicular activity or "space walks", which are timeconsuming and dangerous for astronauts. Robots in space can ...
Process Optimization Of Reactive Systems By Partially Reduced SQP Methods
, 1998
"... . The increasing demand for optimization in process control of reactive systems necessitates the development of fast and reliable software for the numerical computation of optimal controls taking into account the special structures of the chemical systems under investigation. This paper presents a n ..."
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Cited by 1 (1 self)
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. The increasing demand for optimization in process control of reactive systems necessitates the development of fast and reliable software for the numerical computation of optimal controls taking into account the special structures of the chemical systems under investigation. This paper presents a new algorithm based on partially reduced SQP methods for the computation of optimal controls following the direct approach. It is coupled with a package for the simulation of homogeneous reactive systems, which provides the specific routines for the description of the problem at hand. The combined code takes advantage from the fact that the number of influence variables to be determined is rather low compared with the overall number of variables. Numerical results for two new and practically important application problems are presented. Indications for possible further developments are given as well. 1 Motivation and problem formulation Process optimization plays an important role for the ef...
Direct discretization methods for optimization boundary value problems in DAE
"... Practical optimal control problems, e.g., from the areas of robotics or chemical engineering are typically nonlinear and of high dimension. For these problem classes, direct discretization methods have proved to be very efficient and reliable tools. They allow the simultaneous solution of the optimi ..."
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Practical optimal control problems, e.g., from the areas of robotics or chemical engineering are typically nonlinear and of high dimension. For these problem classes, direct discretization methods have proved to be very efficient and reliable tools. They allow the simultaneous solution of the optimization and the simulation task, therefore reducing the amount of computational effort considerably. These direct methods use an apriori discretization of the control functions, e.g., by piecewise polynomials, and of the state functions, e.g., by multiple shooting or collocation. Here, we focus on recent algorithmic developments for the treatment of the resulting large finite dimensional optimization problems. In particular, socalled partially reduced SQP methods are presented as a family of methods including full SQP as well as pure reduced SQP methods. These methods are apt to be tailored specifically to the structures of the problem at hand. Additionally, multilevel control mesh adaptatio...
A Direct PRSQP Method for Path Planning of Satellite Mounted Robots
"... This paper is concerned with the case of a robot mounted on a satellite with the attitude control system not in operation. This is realistic in the sense that the RMS is often operated with the attitude control system off, to prevent sudden corrections. The problem considered is the construction of ..."
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This paper is concerned with the case of a robot mounted on a satellite with the attitude control system not in operation. This is realistic in the sense that the RMS is often operated with the attitude control system off, to prevent sudden corrections. The problem considered is the construction of point to point maneuvers of the robot, so that the final attitude of the satellite is identical to its initial attitude. The modelling assumptions are that the robot consists of rigid bodies with negligible mass and that the whole system is free floating and at rest in space. It has been shown in [5] that this path planning problem is theoretically solvable. There is no uniqueness to such solutions, and generally there is a continuum of such solutions. The one known solution generated in [5], although feasible, is complex and undesirable. There is a need to develop methods of generating robot paths that have certain desirable properties. In order to generate desirable paths the optimal control problem approach has been developed in [9]. The basic idea is to formulate an objective criterion characterizing the desirable paths, and to use the dynamic equations and initial and final configuration conditions as constraints. This defines an optimal control problem, the solution of which results in the desirable path. min
Process Optimization of Reactive Systems Modeled by Elementary Reactions
"... . A modern approach to model chemically reactive systems is to use a set of elementary reactions relating all chemical species which are involved in the chemical system. This detailed modeling leads to rather large systems of di#erentialalgebraic equations to be treated numerically. This paper prese ..."
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. A modern approach to model chemically reactive systems is to use a set of elementary reactions relating all chemical species which are involved in the chemical system. This detailed modeling leads to rather large systems of di#erentialalgebraic equations to be treated numerically. This paper presents a new algorithm based on partially reduced SQP methods for the computation of optimal controls for reactive processes taking into account the specific problem structures at hand. In an exemplary manner we study the formation of ketene from acetic acid. Numerical results for this new and practically important application problem are presented. 1 Introduction Process optimization plays an important role for the e#cient use of resources or the minimization of undesired byproducts in chemical engineering. In this paper we study formation of ketene from acetic acid as a practical example for reactive systems to be optimized with respect to the timedependent process temperature, as well as...
A Discrete Mechanics Approach to Gait Generation on Periodically Unlevel Grounds for the Compasstype Biped Robot
"... Abstract—This paper addresses a gait generation problem for the compasstype biped robot on periodically unlevel grounds. We first derive the continuous/discrete compasstype biped robots (CCBR/DCBR) via continuous/discrete mechanics, respectively. Next, we formulate a optimal gait generation proble ..."
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Abstract—This paper addresses a gait generation problem for the compasstype biped robot on periodically unlevel grounds. We first derive the continuous/discrete compasstype biped robots (CCBR/DCBR) via continuous/discrete mechanics, respectively. Next, we formulate a optimal gait generation problem on periodically unlevel grounds for the DCBR as a finite dimensional nonlinear optimization problem, and show that a discrete control input can be obtained by solving the optimization problem with the sequential quadratic programming. Then, we develop a transformation method from a discrete control input into a continuous zeroorder hold input based on the discrete Lagranged’Alembert principle. Finally, we show numerical simulations, and it turns out that our new method can generate a stable gaits on a periodically unlevel ground for the CCBR. I.