In this paper the solution of nonlinear programming problems by a Sequential Quadratic Programming (SQP) trust-region algorithm is considered. The aim of the present work is to promote global convergence without the need to use a penalty function. Instead, a new concept of a "filter" is introduced which allows a step to be accepted if it reduces either the objective function or the constraint violation function. Numerical tests on a wide range of test problems are very encouraging and the new algorithm compares favourably with LANCELOT and an implementation of Sl 1 QP.

this paper we examine the underlying ideas of the SQP method and the theory that establishes it as a framework from which effective algorithms can

Abstract. This paper describes a software implementation of Byrd and Omojokun’s trust region algorithm for solving nonlinear equality constrained optimization problems. The code is designed for the efficient solution of large problems and provides the user with a variety of linear algebra techniques for solving the subproblems occurring in the algorithm. Second derivative information can be used, but when it is not available, limited memory quasi-Newton approximations are made. The performance of the code is studied using a set of difficult test problems from the CUTE collection.

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Mathematical programs with nonlinear complementarity constraints are reformulated using better-posed but nonsmooth constraints. We introduce a class of functions, parameterized by a real scalar, to approximate these nonsmooth problems by smooth nonlinear programs. This smoothing procedure has the extra benefits that it often improves the prospect of feasibility and stability of the constraints of the associated nonlinear programs and their quadratic approximations. We present two globally convergent algorithms based on sequential quadratic programming, SQP, as applied in exact penalty methods for nonlinear programs. Global convergence of the implicit smooth SQP method depends on existence of a lower-level nondegenerate (strictly complementary) limit point of the iteration sequence. Global convergence of the explicit smooth SQP method depends on a weaker property, i.e. existence of a limit point at which a generalized constraint qualification holds. We also discuss some practical matter...

. Extension of quasi-Newton techniques from unconstrained to constrained optimization via Sequential Quadratic Programming (SQP) presents several difficulties. Among these are the possible inconsistency, away from the solution, of first order approximations to the constraints, resulting in infeasibility of the quadratic programs; and the task of selecting a suitable merit function, to induce global convergence. In the case of inequality constrained optimization, both of these difficulties disappear if the algorithm is forced to generate iterates that all satisfy the constraints, and that yield monotonically decreasing objective function values. (Feasibility of the successive iterates is in fact required in many contexts such as in real-time applications or when the objective function is not well defined outside the feasible set). It has been recently shown that this can be achieved while preserving local two-step superlinear convergence. In this note, the essential ingredients for an S...

This paper considers the solution of Mixed Integer Nonlinear Programming (MINLP) problems. Classical methods for the solution of MINLP problems decompose the problem by separating the nonlinear part from the integer part. This approach is largely due to the existence of packaged software for solving Nonlinear Programming (NLP) and Mixed Integer Linear Programming problems. In contrast, an integrated approach to solving MINLP problems is considered here. This new algorithm is based on branch-and-bound, but does not require the NLP problem at each node to be solved to optimality. Instead, branching is allowed after each iteration of the NLP solver. In this way, the nonlinear part of the MINLP problem is solved whilst searching the tree. The nonlinear solver that is considered in this paper is a Sequential Quadratic Programming solver. A numerical comparison of the new method with nonlinear branch-and-bound is presented and a factor of about 3 improvement over branch-and-bound is observed...

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Traditional design rules for cellular networks are not directly applicable to code division multiple access (CDMA) networks where intercell interference is not mitigated by cell placement and careful frequency planning. For transmission quality requirements, a minimum signal-to-interference ratio (SIR) must be achieved. The base-station location, its pilot-signal power (which determines the size of the cell), and the transmission power of the mobiles all affect the received SIR. In addition, because of the need for power control in CDMA networks, large cells can cause a lot of interference to adjacent small cells, posing another constraint to design. In order to maximize the network capacity associated with a design, we develop a methodology to calculate the sensitivity of capacity to base-station location, pilot-signal power, and transmission power of each mobile. To alleviate the problem caused by different cell sizes, we introduce the power compensation factor, by which the nominal power of the mobiles in every cell is adjusted. We then use the calculated sensitivities in an iterative algorithm to determine the optimal locations of the base stations, pilot-signal powers, and power compensation factors in order to maximize capacity. We show examples of how networks using these design techniques provide higher capacity than those designed using traditional techniques.