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TrustRegion InteriorPoint SQP Algorithms For A Class Of Nonlinear Programming Problems
 SIAM J. CONTROL OPTIM
, 1997
"... In this paper a family of trustregion interiorpoint SQP algorithms for the solution of a class of minimization problems with nonlinear equality constraints and simple bounds on some of the variables is described and analyzed. Such nonlinear programs arise e.g. from the discretization of optimal co ..."
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Cited by 35 (8 self)
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In this paper a family of trustregion interiorpoint SQP algorithms for the solution of a class of minimization problems with nonlinear equality constraints and simple bounds on some of the variables is described and analyzed. Such nonlinear programs arise e.g. from the discretization of optimal control problems. The algorithms treat states and controls as independent variables. They are designed to take advantage of the structure of the problem. In particular they do not rely on matrix factorizations of the linearized constraints, but use solutions of the linearized state equation and the adjoint equation. They are well suited for large scale problems arising from optimal control problems governed by partial differential equations. The algorithms keep strict feasibility with respect to the bound constraints by using an affine scaling method proposed for a different class of problems by Coleman and Li and they exploit trustregion techniques for equalityconstrained optimizatio...
Addressing Multiobjective Control: Safety and Performance Through Constrained Optimization
"... . We address systems which have multiple objectives: broadly speaking, these objectives can be thought of as safety and performance goals. Guaranteeing safety is our first priority, satisfying performance criteria our second. In this paper, we compute the system's safe operating space and repres ..."
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Cited by 8 (1 self)
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. We address systems which have multiple objectives: broadly speaking, these objectives can be thought of as safety and performance goals. Guaranteeing safety is our first priority, satisfying performance criteria our second. In this paper, we compute the system's safe operating space and represent it in closed form, and then, within this space, we compute solutions which optimize a given performance criterion. We describe the methodology and illustrate it with two examples of systems in which safety is paramount: a twoaircraft collision avoidance scenario and the flight management system of a VSTOL aircraft. In these examples, performance criteria are met using mixedinteger nonlinear programming (MINLP) and nonlinear programming (NLP), respectively. Optimized trajectories for both systems demonstrate the effectiveness of this methodology on systems whose safety is critical. 1
On InteriorPoint Newton Algorithms For Discretized Optimal Control Problems With State Constraints
 OPTIM. METHODS SOFTW
, 1998
"... In this paper we consider a class of nonlinear programming problems that arise from the discretization of optimal control problems with bounds on both the state and the control variables. For this class of problems, we analyze constraint qualifications and optimality conditions in detail. We derive ..."
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Cited by 7 (2 self)
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In this paper we consider a class of nonlinear programming problems that arise from the discretization of optimal control problems with bounds on both the state and the control variables. For this class of problems, we analyze constraint qualifications and optimality conditions in detail. We derive an affinescaling and two primaldual interiorpoint Newton algorithms by applying, in an interiorpoint way, Newton's method to equivalent forms of the firstorder optimality conditions. Under appropriate assumptions, the interiorpoint Newton algorithms are shown to be locally welldefined with a qquadratic rate of local convergence. By using the structure of the problem, the linear algebra of these algorithms can be reduced to the null space of the Jacobian of the equality constraints. The similarities between the three algorithms are pointed out, and their corresponding versions for the general nonlinear programming problem are discussed.
A Reduced Space Interior Point Strategy for Optimization of Differential Algebraic Systems
 Computers & Chemical Engineering
, 1999
"... A novel nonlinear programming (NLP) strategy is developed and applied to the optimization of differential algebraic equation (DAE) systems. Such problems, also referred to as dynamic optimization problems, are common in chemical process engineering and remain challenging applications of nonlinear pr ..."
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Cited by 6 (3 self)
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A novel nonlinear programming (NLP) strategy is developed and applied to the optimization of differential algebraic equation (DAE) systems. Such problems, also referred to as dynamic optimization problems, are common in chemical process engineering and remain challenging applications of nonlinear programming. These applications often consist of large, complex nonlinear models that result from discretizations of DAEs. Variables in the NLP model include state and control variables, with far fewer control variables than states. Moreover, all of these discretized variables have associated upper and lower bounds which can be potentially active. To deal with this large, highly constrained problem, an interior point NLP strategy is developed. Here a log barrier function is used to deal with the large number of bound constraints in order to transform the problem to an equality constrained NLP. A modified Newton method is then applied directly to this problem. In addition, this method uses an efficient decomposition of the discretized DAEs and the solution of the Newton step is performed in the reduced space of the independent variables. The resulting approach exploits many of the features of the DAE system and is performed element by element in a forward manner. Several large dynamic process optimization problems are considered to demonstrate the effectiveness of this approach; these include complex separation and reaction processes (including reactive distillation) with several hundred DAEs. NLP formulations with over 55,000 variables are considered. These problems are solved in 5 to 12 CPU minutes on small workstations. Key words: interior point; dynamic optimization; nonlinear programming 1 1
SQP SAND Strategies that Link to Existing Modeling Systems
"... Introduction Engineering modeling systems form the cornerstone of analysis and design in a broad range of disciplines. In computational mechanics and the analysis of transport systems, a wide variety of PDE modeling systems and products are available. In addition to solving discretized partial dier ..."
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Cited by 1 (1 self)
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Introduction Engineering modeling systems form the cornerstone of analysis and design in a broad range of disciplines. In computational mechanics and the analysis of transport systems, a wide variety of PDE modeling systems and products are available. In addition to solving discretized partial dierential equations, most of these also have capabilities for mesh generation, many options for construction of nite element bases and a wide variety of linear iterative solvers and preconditioners. These engineering systems represent dozens of manyears of software development. However, virtually all of them were developed for analysis and not for design optimization. As a result, there remain some interesting challenges in leveraging this software investment in order to adapt these systems for optimization. In principle, such systems require smooth functions and rst (and possibly second) derivatives to be accessed from the modeling equations by the nonlinear programming (NLP) algor