Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems with general inequality constraints (linear and nonlinear). We assume that first derivatives are available, and that the constraint gradients are sparse.

In this paper a family of trust-region interior-point 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 trust--region techniques for equality-constrained optimizatio...

A novel algorithm for buffer management and packet scheduling is presented for providing loss and delay differentiation for traffic classes at a network router. The algorithm, called JoBS (Joint Buffer Management and Scheduling) , provides delay and loss differentiation independently at each node, without assuming admission control or policing. The novel capabilities of the proposed algorithm are that (1) scheduling and buffer management decisions are performed in a single step, and (2) both relative and (whenever possible) absolute QoS requirements of classes are supported. Numerical simulation examples, including results for a heuristic approximation, are presented to illustrate the effectiveness of the approach and to compare the new algorithm to existing methods for loss and delay differentiation.

A novel algorithm for buffer management and rate allocation is presented for providing loss and delay differentiation for traffic classes at a network router. The algorithm, called JoBS, provides delay and loss differentiation independently at each node, without assuming admission control or policing. Contrary to most existing algorithms, scheduling and buffer management decisions are performed in a single step. Both relative

. In recent years, general-purpose sequential quadratic programming (SQP) methods have been developed that can reliably solve constrained optimization problems with many hundreds of variables and constraints. These methods require remarkably few evaluations of the problem functions and can be shown to converge to a solution under very mild conditions on the problem. Some practical and theoretical aspects of applying general-purpose SQP methods to optimal control problems are discussed, including the influence of the problem discretization and the zero/nonzero structure of the problem derivatives. We conclude with some recent approaches that tailor the SQP method to the control problem. Key words. large-scale optimization, sequential quadratic programming (SQP) methods, optimal control problems, multiple shooting methods, single shooting methods, collocation methods AMS subject classifications. 49J20, 49J15, 49M37, 49D37, 65F05, 65K05, 90C30 1. Introduction. Recently there has been c...

This paper presents a general framework for maximally decimated modulated filter banks. The theory covers the known classes of cosine modulation and relates them to complexmodulated filter banks. The prototype filters have arbitrary lengths, and the overall delay of the filter bank is arbitrary, within fundamental limits. Necessary and sufficient conditions for perfect reconstruction (PR) are derived using the polyphase representation. It is shown that these PR conditions are identical for all types of modulation---modulation based on the discrete cosine transform (DCT), both DCT-III/DCT-IV and DCT-I/DCT-II, and modulation based on the modified discrete Fourier transform (MDFT). A quadratic-constrained design method for prototype filters yielding PR with arbitrary length and system delay is derived, and design examples are presented to illustrate the tradeoff between overall system delay and stopband attenuation (subchannelization). Index Terms---Cosine-modulated filter bank, DCT, filter bank, MDCT, modulated filter bank. I.

We propose a sequential quadratic programming (SQP) method for the optimal control of large-scale dynamical systems. The method uses modified multiple shooting to discretize the dynamical constraints. When these systems have relatively few parameters, the computational complexity of the modified method is much less than that of standard multiple shooting. Moreover, the proposed method is demonstrably more robust than single shooting. In the context of the SQP method, the use of modified multiple shooting involves a transformation of the constraint Jacobian. The affected rows are those associated with the continuity constraints and any path constraints applied within the shooting intervals. Path constraints enforced at the shooting points (and other constraints involving only discretized states) are not transformed. The transformation is cast almost entirely at the user level and requires minimal changes to the optimization software. We show that the modified quadratic subproblem yields a descent direction for the l_1 penalty function. Numerical experiments verify the efficiency of the modified method.

A novel framework, called JoBS (Joint Buffer Management and Scheduling), is presented for reasoning about relative and absolute per-class service differentiation in a packet network without information on traffic arrivals. JoBS has two unique capabilities: (1) JoBS makes scheduling and buffer management decisions in a single step, and (2) JoBS supports both relative and absolute QoS requirements of classes. JoBS is presented in terms of the solution to an optimization problem. Numerical simulation examples, including results for a heuristic approximation of JoBS, are presented to illustrate the effectiveness of the approach and to compare JoBS to existing methods for loss and delay differentiation.

Abstract—In this paper, we study cooperation among the adjacent base stations (BSs) for downlink scheduling in code division multiple access cellular networks. We propose a cooperative fair scheduling scheme, namely, cooperative utility fair scheduling, to increase multiuser diversity gain and reduce interference among BSs. The scheduler maintains fairness and smooth service delivery by balancing the long-term average throughput of users. Monte Carlo simulation results are given to demonstrate the effectiveness of the proposed scheme in terms of multiuser diversity gain, throughput, and fairness. Index Terms—Code division multiple access (CDMA) cellular networks, cooperative communications, fair scheduling, Monte Carlo simulations. I.

In the broad context of modeling for system design, it is normally assumed that all decision-makers cooperate fully and thus avoid conflict. However, this is not always possible, in which case the design process is best modelled and studied as a multi-player game. The objective in this paper is to present and illustrate such a general game-theoretic framework for design modeling. In particular, explicit solutions are computed and interpreted for conservative or minmax, Pareto, Nash and Stackelberg games in a simple pressure vessel design example in which two players interact strategically, one of whom wants to minimize the weight and other wishes to maximize the volume. In another example in which a rotating disk is to be optimized for two objectives related to its design and manufacture, the Pareto solutions show how a novel manufacturing cost function can improve, under assumptions of a cooperative game, the optimal shape that is obtained under a single objective formulation related ...