Institute for Systems Research Technical Reports
Permanent URI for this collectionhttp://hdl.handle.net/1903/4376
This archive contains a collection of reports generated by the faculty and students of the Institute for Systems Research (ISR), a permanent, interdisciplinary research unit in the A. James Clark School of Engineering at the University of Maryland. ISR-based projects are conducted through partnerships with industry and government, bringing together faculty and students from multiple academic departments and colleges across the university.
Browse
19 results
Search Results
Item User's Guide for CFSQP Version 2.0: A C Code for Solving (Large Scale) Constrained Nonlinear (Minimax) Optimization Problems, Generating Iterates Satisfying All Inequality Constraints(1994) Lawrence, Craig T.; Zhou, J.L.; Tits, A.L.; ISRCFSQP is a set of C functions for the minimization of the maximum of a set of smooth objective functions (possibly a single one) subject to general smooth constraints. If the initial guess provided by the user is infeasible for some inequality constraint or some linear equality constraint, CFSQP first generates a feasible point for these constraints; subsequently the successive iterates generated by CFSQP all satisfy these constraints. Nonlinear equality constraints are turned into inequality constraints (to be satisfied by all iterates) and the maximum of the objective functions is replaced by an exact penalty function which penalizes nonlinear equality constraint violations only. When solving problems with many sequentially related constraints (or objectives), such as discretized semi- infinite programming (SIP) problems, CFSQP gives the user the option to use an algorithm that efficiently solves these problems, greatly reducing computational effort. The user has the option of either requiring that the objective function (penalty function if nonlinear equality constraints are present) decrease at each iteration after feasibility for nonlinear inequality and linear constraints has been reached (monotone line search), or requiring a decrease within at most four iterations (nonmonotone line search). He/She must provide functions that define the objective functions and constraint functions and may either provide functions to compute the respective gradients or require that CFSQP estimate them by forward finite differences.CFSQP is an implementation of two algorithms based on Sequential Quadratic Programming (SQP), modified so as to generate feasible iterates. In the first one (monotone line search), a certain Armijo type arc search is used with the property that the step of one is eventually accepted, a requirement for superlinear convergence. In the second one the same effect is achieved by means of a "nonmonotone" search along a straight line. The merit function used in both searches is the maximum of the objective functions if there is no nonlinear equality constraints, or an exact penalty function if nonlinear equality constraints are present.
Item An SQP Algorithm for Finely Discretized Continuous Minimax Problems and Other Minimax Problems with Many Objective Functions(1993) Zhou, J.L.; Tits, A.L.; ISRA common strategy for achieving global convergence in the solution of semi-infinite programming (SIP) problems, and in particular of continuous minimax problems, is to (approximately) solve a sequence of discretized problems, with a progressively finer discretization mesh. Finely discretized minimax and SIP problems, as well as other problems with many more objectives/constraints than variables, call for algorithms in which successive search directions are computed based on a small but significant subset of the objectives/constraints, with ensuing reduced computing cost per iteration and decreased risk of numerical difficulties. In this paper, an SQP-type algorithm is proposed that incorporates this idea in the particular case of minimax problems. The general case will be considered in a separate paper. The quadratic programming subproblem that yields the search direction involves only a small subset of the objectives functions. This subset is updated at each iteration in such a way that global convergence is insured. Heuristics are suggested that take advantage of a possible close relationship between ﲡdjacent objective functions. Numerical results demonstrate the efficiency of the proposed algorithm.Item On the Computation of the Real Stability Radius(1993) Yang, Y.; Tits, A.L.; Qiu, L.; ISRRecently, Qiu et al. obtained a computationally attractive formula for the computation of the real stability radius. This formula involves a global maximization over frequency. Here we show that the frequency range can be limited to a certain finite interval. Numerical experimentation suggests that this interval is often reasonably small.Item A Simple quadratically convergent Interior Point Algorithm for Linear Programming and Convex quadratic Programming(1993) Tits, A.L.; Zhou, J.L.; ISRAn algorithm for linear programming (LP) and convex quadratic programming (CQP) is proposed, based on an interior point iteration introduced more than ten years ago by J. Herskovits for the solution of nonlinear programming problems. Herskovits' iteration can be simplified significantly in the LP/CQP case, and quadratic convergence from any initial point can be achieved. Interestingly the resulting algorithm is closely related to a popular scheme, proposed in 1989 by Kojima et al. independently of Herskovits' work.Item User's Guide for JAKEFSQP Version 1.0(1993) Mathur, P.D.; Tits, A.L.; ISRJAKEFSQP is a utility program that allows a user of the FSQP constrains optimization routines to involve the automatic differentiation preprocessor JAKEF with minimal burden.Item An SQP Algorithm for Finely Discretized SIP Problems and Other Problems with Many Constraints(1992) Zhou, J.L.; Tits, A.L.; ISRA Common strategy for achieving global convergence in the solution of semi-infinite programming (SIP) problems is to (approximately) solve a sequence of discretized problems, with a progressively finer discretization mesh. Finely discretized SIP problems, as well as other problems with many more constraints than variables, call for algorithms in which successive search directions are computed based on a small but significant subset of the constraints, with ensuing reduced computing cost per iteration and decreased risk of numerical difficulties. In this paper, an SQP-type algorithm is proposed that incorporates this idea. The quadratic programming subproblem that yields the search direction involves only a small subset of the constraints. This subset is updated at each iteration in such a way that global convergence is insured. Heuristics are suggested that take advantage of possible close relationship between "adjacent" constraints. Numerical results demonstrate the efficiency of the proposed algorithm.Item User's Guide for FSQP Version 3.0c: A FORTRAN Code for Solving Constrained Nonlinear (Minimax) Optimization Problems, Generating Iterates Satisfying All Inequality and Linear Constraints(1992) Zhou, J.L.; Tits, A.L.; ISRFSQP 3.0c is a set of FORTRAN subroutines for the minimization of the maximum of a set of smooth objective functions (possibly a single one) subject to general smooth constraints. If the initial guess provided by the user is infeasible for some inequality constraint or some linear equality constraint, FSQP first generates a feasible point for these constraints; subsequently the successive iterates generated by FSQP all satisfy these constraints. Nonlinear equality constraints are turned into inequality constraints (to be satisfied by all iterates) and the maximum of the objective functions is replaced by an exact penalty function which penalizes nonlinear equality constraint violations only. The user has the option of either requiring that the (modified) objective function decrease at each iteration after feasibility for nonlinear inequality and linear constraints has been reached (monotone line search), or requiring a decrease within at most four iterations (nonmonotone line search). He/She must provide subroutines that define the objective functions and constraint functions and may either provide subroutines to compute the gradients of these functions or require that FSQP estimate them by forward finite differences.FSQP 3.0c implements two algorithms based on Sequential Quadratic Programming (SQP), modified so as to generate feasible iterates. In the first one (monotone line search), a certain Armijo type arc search is used with the property that the step of one is eventually accepted, a requirement for superlinear convergence. In the second one the same effect is achieved by means of a (nonmonotone) search along a straight line. The merit function used in both searches is the maximum of the objective functions if there is no nonlinear equality constraint.
Item When is the Multiaffine Image of a Cube a Polygon?(1992) Tsing, N-K.; Tits, A.L.; ISRWe give two simple sufficient conditions under which the multiaffine image on the complex plane of an m-dimensional cube is a convex polygon. A third condition which, in some generic sense, is necessary and sufficient is then obtained. The conditions involve checking the locations of the image of the vertices of the cube. These results help determine whether a family of parametrized polynomials is stable, and provide a tool for robust control analysis.Item On Continuity/Discontinuity in Robustness Indicators(1991) Lee, Li; Tits, A.L.; ISRContinuity/discontinuity of robustness indicators is reviewed. For the case of real or mixed uncertainty, a regularization of the frequency dependent robustness margin is proposed and its properties are discussed. Implication of this regularization in the case of polynomial families with affine dependency on the uncertainty is pointed out.Item A Measure of Worst-Case HPerformance and of Largest Acceptable Uncertainty(1991) Fan, Michael K-H.; Tits, A.L.; ISRThe structured singular value (SSV or ) is know to be an effective tool for assessing robust performance of linear time- invariant models subject to structured uncertainty. Yet all a single analysis provides is a bound ݠon the uncertainty under which stability as well as Hperformance level of k/ݠare guaranteed, where k is preselectable. In this paper, we introduce a related quantity, denoted by v which provides answers for the following questions: (i) given ݬ determine the smallest with the peoperty that, for any uncertainty bounded by ݬ an H performance level of