### Browsing by Author "Zhou, J."

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Item Fast Feasible Direction Methods, with Engineering Applications(1991) Tits, A.L.; Zhou, J.; ISROptimization problems arising in engineering applications often present distinctive features that are not exploited, or not accounted for, in standard numerical optimization algorithms and software codes. First, in many cases, equality constraints are not present, or can be simply eliminated. Second, there are several instances where it is advantageous, or even crucial, that, once a feasible point has been achieved, all subsequent iterates be feasible as well. Third, many optimization problems arising engineering are best formulated as constrained minimax problems. Fourth, some specifications must be achieved over a range of values of an independent parameter (functional constraints).While various other distinctive features arise in optimization problems found in specific classes of engineering problems, this paper focuses on those identified above, as they have been the object of special attention by the authors and their co-workers in recent years. Specifically, a basic scheme for efficiently tackling inequality constrained optimization while forcing feasible iterates is discussed and various extensions are proposed to handle the distinctive features just pointed out.

Item Fast, Globally Convergent Optimization Algorithms, with Application to Engineering System Design(1992) Zhou, J.; Tits, A.L.; ISRComplex engineering system design usually involves multiple objective specifications. Tradeoffs have to be made among these specifications, possibly under constraints, as they oftentimes compete with one another. It has been realized that these problems can be faithfully translated into (inequality) constrained minimax problems, or a sequence of such problems and then the originally design problems can be solved with the support of numerical optimization techniques. This dissertation develops a number of optimization algorithms for the solution of these problems, with emphasis on many distinctive features of engineering systems that existing optimization algorithms have not fully exploited or accounted for. Efforts are made to maintain "desirable" analytic properties that existing popular optimization algorithms enjoy.Algorithms are developed in a very general setup, yet specialized to indicate the direct connections with different branches of engineering applications. The adaptation of advanced optimization techniques, such as feasible sequential quadratic programming (FSQP) and nonmonotone line search (NLS), to the solution of engineering problems are carefully addressed. Efficiency of these algorithms has been given high priority in the development, since it is usually very time-consuming to evaluate specifications in engineering applications.

In the presence of functional specifications, i.e., specifications that are to be satisfied over an interval of a free parameter such as time or frequency (shaping of time or frequency response, for instance), an efficient algorithm is proposed that significantly outperforms the existing algorithms in the same context. This algorithm has been successfully applied for the solution of many engineering problems in the context of optimization-based system design.

These new algorithms are satisfactorily characterized by conventional notions of optimization such as global convergence and rate of local convergence. Interesting and meaningful results on the rate of local convergence are obtained with the aid of nonmonotone line search. The performance of these algorithms represented by extensive numerical experiments measures up to the theoretic analysis.

A number of feedback system design problems are provided to illustrate the efficiency and applicability of these algorithms.

Item A Note on the Positive Definiteness of BFGS Update in Constrained Optimization(1990) Zhou, J.; Tits, A.L.; ISRThis note reviews a few existing methods to maintain the positive definiteness of BFGS in constrained optimization, and their impacts on both global and local convergence. The boundedness of the matrix from above is also briefly addressed. Some new strategies are proposed. Convergence analysis and numerical examples are not included.Item User's Guide for FSQP Version 2.0 A Fortran Code for Solving Optimization Problems, Possibly Minimax, with General Inequality Constraints and Linear Equality Constraints, Generating Feasible Iterates(1990) Zhou, J.; Tits, A.L.; ISRFSQP 2.0 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 nonlinear smooth inequality constraints, linear inequality and linear equality constraints, and simple bounds on the variables. If the initial guess provided by the user is infeasible, FSQP first generates a feasible point; subsequently the successive iterates generated by FSQP all satisfy the constraints. The user has the option of requiring that the maximum value among the objective functions decrease at each iteration after feasibility has been reached (monotone 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 2.0 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 a objective functions.Item User's Guite for FSQP Version 1.0: A Fortran Software for Solving Optimization Problems with General Inequality Constraints and Linear Equality Constraints, Generating Feasible Iterates.(1989) Zhou, J.; Tits, A.L.; ISRFSQP is a set of Fortran subroutines for the minimization of a smooth objective function subject to nonlinear smooth inequality constraints, linear inequality and linear equality constraints, and simple bounds on the variables. If the initial guess provided by the user is infeasible, FSQP first generates a feasible point from the given point. Subsequently the successive iterates generated by FSQP all satisfy the constraints. The user also has the option of requiring that the objective value decrease at each iteration after feasibility has been reached. The user must provide subroutines that define the objective and constraint functions and may either provide the subroutines that define the gradients of these functions or require that FSQP estimate them by forward finite differences. FSQP uses an algorithm based on Sequential Quandratic Programming (SQP), modified so as to generate feasible iterates. A certain arc search ensures that the step of one is eventually satisfied, a requirement for superlinear convergence. The merit function used in this arc search is the objective function itself, and either an Armijo- type line search or a nonmonotone line search borrowed from Grippo et al. may be selected.