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.

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Author: search.filters.author.Tits, A.L.End date: 1999

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Now showing 1 - 10 of 53
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    A Primal-Dual Interior-Point Method for Nonconvex Optimization with Multiple Logarithmic Barrier Parameters and with Strong Convergence Properties
    (1998) Urban, T.; Tits, A.L.; Lawrence, Craig T.; ISR
    It is observed that an algorithm proposed in the 1980s for thesolution of nonconvex constrained optimization problems is in fact aprimal-dual logarithmic barrier interior-point method closely related tomethods under current investigation in the research community. Its maindistinguishing features are judicious selection and update of the multiplebarrier parameters (one per constraint), use of the objective function asmerit function, and careful bending of the search direction. As a payoff,global convergence and fast local convergence ensue. The purpose of thisshort note is to describe the algorithm in the interior-point framework andlanguage and to provide a preliminary numerical evaluation. The latter showsthat the method compares well with algorithms recently proposed by otherresearch groups.
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    User's Guide for ADIFFSQP Version 0.91
    (1997) Liu, Mingyan D.; Tits, A.L.; ISR
    ADIFFSQP is a utility program that allows to user of the FFSQP[1] constrained nonlinear optimization routines to invoke the computational differentiation (or automatic differentiation:AD) preprocessor ADIFOR2.0 [2] conveniently
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    Absolute Stability Theory, Theory, and State-Space Verification of Frequency-Domain Conditions: Connections and Implications for Computation
    (1997) Chou, Y.S.; Tits, A.L.; Balakrishnan, V.; ISR
    The main contribution of the paper is to show the equivalence between the following two approaches for obtaining sufficient conditions for the robust stability of systems with structured uncertainties: (i) apply the classical absolute stability theory with multipliers; (ii) use the modern theory, specifically, the upper bound obtained by Fan, Tits and Doyle [IEEE TAC, Vol. 36, 25-38]. In particular, the relationship between the stability multipliers used in absolute stability theory and the scaling matrices used in the cited reference is explicitly characterized. The development hinges on the derivation of certain properties of a parameterized family of complex LMIs (linear matrix inequalities), a result of independent interest. The derivation also suggests a general computational framework for checking the feasibility of a broad class of frequency- dependent conditions, and in particular, yields a sequence of computable ﲭixed- -norm upper bounds , defined with guaranteed convergence from above to the supremum over frequency of the aforementioned upper bound.
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    Feasible Sequential Quadratic Programming for Finely Discretized Problems from SIP
    (1997) Lawrence, Craig T.; Tits, A.L.; ISR
    A sequential Quadratic Programming algorithm designed to efficiently solve nonlinear optimization problems with many inequality constraints, e.g. problems arising from finely discretized Semi-Infinite Programming, is described and analyzed. The key features of the algorithm are (i) that only a few of the constraints are used in the QP sub-problems at each iteration, and (ii) that every iterate satisfies all constraints.
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    Multiobjective Optimization of a Leg Mechanism with Various Spring Configurations for Force Reduction
    (1996) Shieh, W-B.; Azarm, Shapour; Tsai, L-W.; Tits, A.L.; ISR
    In this paper, the design of a two degree-of-freedom leg mechanism is accomplished by a two-stage optimization process. In the first stage, leg dimensions are optimized with respect to three design objectives: minimize (i) leg size, (ii) vertical actuating force, and (iii) peak crank torque for an entire walking cycle. Following the optimization of leg dimensions, in the second stage, spring elements with various placement configurations are considered for further reduction of the actuating force and crank torque. Several tradeoff solutions are obtained and a comparison between variously spring configurations is made. It is shown that the inclusion of spring elements can significantly reduce the actuating force and crank torque.
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    A New Class of Six-Bar Mechanisms with Symmetrical Coupler Curves
    (1996) Shieh, W-B.; Azarm, Shapour; Tsai, L-W.; Tits, A.L.; ISR
    A new class of six-bar mechanisms with symmetrical coupler-point curves is presented. This class of mechanisms is made up of a four-bar linkage with an additional dyad to form an embedded regular or skew pantograph. Because the coupler curve generated at an output point is amplified from that of a four-bar, a compact mechanism with a relatively large coupler curve can be obtained. In addition, due to their structure arrangement, the analysis and synthesis of such mechanisms can be easily achieved. It is shown that the admissible range of transmission angle for such mechanisms is smaller than that of a four-bar mechanism. It is also shown that mechanisms with an embedded skew pantograph exhibit better design flexibility than those with an embedded regular pantograph. Finally, an example mechanism from this class is illustrated and compared with a four-bar linkage with the same coupler curve.
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    Robustness under Bounded Uncertainty with Phase Information
    (1996) Tits, A.L.; Balakrishnan, V.; Lee, Li; ISR
    We consider uncertain linear systems where the uncertainties, in addition to being bounded, also satisfy constraints on their phase. In this context, we define the ﲰhase-sensitive structured singular value (PS-SSV) of a matrix, and show that sufficient (and sometime necessary) conditions for stability of such uncertain linear systems can be rewritten as conditions involving PS-SSV. We then derive upper bounds for PS-SSV, computable via convex optimization. We extend these results to the case where the uncertainties are structured (diagonal or block-diagonal, for instance).
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    Globally Convergent Algorithms for Robust Pole Assignment by State Feedback
    (1995) Tits, A.L.; Yang, Y.; ISR
    It is observed that an algorithm proposed in 1985 by Kautsky, Nichols and Van Dooren (KNV) amounts to maximize, at each iteration, the determinant of the candidate closed-loop eigenvector matrix X with respect to one of its columns (with unit length constraint), subject to the constraint that it remains a valid closed-loop eigenvector matrix. This interpretation is used to prove convergence of the KNV algorithm. It is then shown that a more efficient algorithm is obtained if det (X) is concurrently maximized with respect to two columns of X, and that such a scheme is easily extended to the case where the eigenvalues to be assigned include complex conjugate pairs. Variations exploiting the availability of multiple processors are suggested. Convergence properties of the proposed algorithms are established. Their superiority is demonstrated numerically.
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    Nonlinear Equality Constraints in Feasible Sequential Quadratic Programming
    (1995) Lawrence, Craig T.; Tits, A.L.; ISR
    A simple scheme is proposed for handling nonlinear equality constraints in the context of a previously introduced sequential quadratic programming (SQP) algorithm for inequality constrained problems, generating iterates satisfying all constraints. The key is an idea due to Mayne and Polak (Math. progr., vol. 11, pp 67- 80, 1976) by which nonlinear equality constraints are treated as ﳣﱠtype constraints to be satisfied by all iterates, thus precluding any positive value, and an exact penalty term is added to the objective function which penalizes negative values. Mayne and Polak obtain a suitable value of the penalty parameter by iterative adjustments based on a test involving estimates of the KKT multipliers. We argue that the SQP framework allows for a more effective estimation of these multipliers, and we provide convergence analysis of the resulting algorithms. Numerical results, obtained with the FSQP/CFSQP code, are reported.
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    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.; ISR
    CFSQP 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.