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...

Abstract not found

In this paper, the filter technique of Fletcher and Leyffer (1997) is used to globalize the primaldual interior-point algorithm for nonlinear programming, avoiding the use of merit functions and the updating of penalty parameters. The new algorithm decomposes the primal-dual step obtained from the perturbed first-order necessary conditions into a normal and a tangential step, whose sizes are controlled by a trust-region type parameter. Each entry in the filter is a pair of coordinates: one resulting from feasibility and centrality, and associated with the normal step; the other resulting from optimality (complementarity and duality), and related with the tangential step. Global convergence to first-order critical points is proved for the new primal-dual interior-point filter algorithm.

Identification of transcription factor binding sites (regulatory motifs) is a major interest in contemporary biology. We propose a new likelihood based method, COMODE, for identifying structural motifs in DNA sequences. Commonly used methods (e.g. MEME, Gibbs motif sampler) model binding sites as families of sequences described by a position weight matrix (PWM) and identify PWMs that maximize the likelihood of observed sequence data under a simple multinomial mixture model. This model assumes that the positions of the PWM correspond to independent multinomial distributions with four cell probabilities. We address supervising the search for DNA binding sites using the information derived from structural characteristics of protein-DNA interactions. We extend the simple multinomial mixture model to a constrained multinomial mixture model by incorporating constraints on the information content profiles or on specific parameters of the motif PWMs. The parameters of this extended model are estimated by maximum likelihood using a nonlinear constraint optimization method. Likelihood-based cross-validation is used to select model parameters such as motif width and constraint type. The performance of COMODE is compared with existing motif detection methods on simulated data that incorporate real motif examples from Saccharomyces cerevisiae. The proposed method is especially effective when the motif of interest appears as a weak signal in the data. Some of the transcription factor binding data of Lee et al. (2002) were also analyzed using COMODE and biologically verified sites were identified.

In (Boggs, Tolle and Kearsley 1994b) the authors introduced an effective algorithm for general large scale nonlinear programming problems. In this paper we describe the theoretical foundation for this method. The algorithm is based on a trust region, sequential quadratic programming (SQP) technique and uses a special auxiliary function, called a merit function or line-search function, for assessing the steps that are generated. A global convergence theorem for a basic version of the algorithm is stated and its proof is outlined.

Abstract—We propose an algorithm to maximize the instantaneous sum data rate transmitted by a base station in the downlink of a multiuser multiple-input, multiple-output system. The transmitter and the receivers may each be equipped with multiple antennas and each user may receive more than one data stream. We show that maximizing the sum rate is closely linked to minimizing the product of mean squared errors (PMSE). The algorithm employs an uplink/downlink duality to iteratively design transmit-receive linear precoders, decoders, and power allocations that minimize the PMSE for all data streams under a sum power constraint. Numerical simulations illustrate the effectiveness of the algorithm and support the use of the PMSE criterion in maximizing the overall instantaneous data rate. I.

Abstract not found

The optimal design of launch vehicles based on liquid rocket engines is critically dependent on ascent trajectories and thrust throttling. Recently many authors have incorporated trajectory optimization at conceptual design level but still have not gauged the potential of using thrust throttling at conceptual design phase. In this study we propose not only the trajectory optimization but also the thrust throttling at the conceptual design phase. This newly formulation problem is solved through hybrid optimization algorithm using Genetic Algorithm as global optimizer and Sequential Quadratic Programming as local optimizer starting from the solution given by Genetic Algorithm. The objective is to find minimum gross launch weight (GLW), optimal trajectory and thrust throttling profile for liquid fueled space launch vehicle (SLV). The improvement in system design using thrust throttling is studied in detail. 1.

Formulation In the most general form, we can write an optimization problem in a topological space endowed with some topology and J : R is the objective functional. By extending the objective functional to U via J(u) := we can rewrite this problem as .

Abstract—The performance of mobile cellular radio networks is limited by the level of cochannel interference that can be tolerated. The use of antennas arrays is very helpful in enhancing the performance and capacity of the wireless communication system. This paper presents a method for antenna pattern synthesis that suppress multiple interfering narrow or wide band signals while receiving the desired signal by controlling only the phase. Excitation phases are computed using the Sequential Quadratic Programming (SQP) technique. This method transforms the nonlinear minimization (or maximization) problem to a sequence of quadratic subproblems,based on a quadratic approximation of the Lagrangian function. 252 Mouhamadou et al. 1.