Active set truncated-Newton algorithm for simultaneous optimization of distillation column

An active set truncated-Newton algorithm (ASTNA) is proposed to solve the large-scale bound constrained sub-problems. The global convergence of the algorithm is obtained and two groups of numerical experiments are made for the various large-scale problems of varying size. The comparison results between ASTNA and the subspace limited memory quasi-Newton algorithm and between the modified augmented Lagrange multiplier methods combined with ASTNA and the modified barrier function method show the stability and effectiveness of ASTNA for simultaneous optimization of distillation column.

An active set algorithm for nonlinear optimization with polyhedral constraints

A polyhedral active set algorithm PASA is developed for solving a nonlinear optimization problem whose feasible set is a polyhedron. Phase one of the algorithm is the gradient projection method, while phase two is any algorithm for solving a linearly constrained optimization problem. Rules are provided for branching between the two phases. Global convergence to a stationary point is established, while asymptotically PASA performs only phase two when either a nondegeneracy assumption holds, or the active constraints are linearly independent and a strong second-order sufficient optimality condition holds.

The Origin and Tectonic Setting of Precambrian Greywacke of Ribandar-Chimbel, Goa, India： Petrological and Geochemical Evidence

The Precambrian greywacke of Ribandar-Chimbel belonging to the Sanvordem Formation of the Goa Group, India, has been studied for petrography and analyzed for major trace elements. The greywacke is characterized by angular to sub-round grains of quartz, feldspar, biotite, chlorite and clay minerals. The abundance of clay in the matrix seems to have influenced the Al2O3 content and the K20/Al2O3 ratio. The variation diagrams indicate a decreasing trend of TiO2, Al2O3, Fe2O3 and MgO; whereas Na2O and CaO exhibit a scatter which could be a result of the variable presence of feldspar within the sediments. The immobile elements, vanadium （25 to 144 ppm）, nickel （up to 107 ppm） and chromium （up to 184 ppm）, reflect abundance of clay minerals. The greywacke shows strongly fractionated REE patterns with LaN/YbN = 8 to 26 and with higher total REE abundances （up to 245 ppm）. The low REE enrichment and depletion in heavier REE with prominent negative Eu anomaly （Eu/Eu^＊= 0.54 to 0.79） suggest a derivation of the greywacke from an old upper continental crust composed chiefly of felsic components. Petrological evidence and geochemical data suggest that the deposition of the greywacke largely took place in a deep to shallow basin that progressively chang- ed from that of a continental island arc to an active continental setting.

EFFICIENT NONNEGATIVE MATRIX FACTORIZATION VIA MODIFIED MONOTONE BARZILAI-BORWEIN METHOD WITH ADAPTIVE STEP SIZES STRATEGY

In this paper,we develop an active set identification technique.By means of the active set technique,we present an active set adaptive monotone projected Barzilai-Borwein method(ASAMPBB)for solving nonnegative matrix factorization(NMF)based on the alternating nonnegative least squares framework,in which the Barzilai-Borwein(BB)step sizes can be adaptively picked to get meaningful convergence rate improvements.To get optimal step size,we take into account of the curvature information.In addition,the larger step size technique is exploited to accelerate convergence of the proposed method.The global convergence of the proposed method is analysed under mild assumption.Finally,the results of the numerical experiments on both synthetic and real-world datasets show that the proposed method is effective.

A NEW TRUST-REGION ALGORITHM FOR NONLINEAR CONSTRAINED OPTIMIZATION

We propose a new trust region algorithm for nonlinear constrained optimization problems. In each iteration of our algorithm, the trial step is computed by minimizing a quadratic approximation to the augmented Lagrange function in the trust region. The augmented Lagrange function is also used as a merit function to decide whether the trial step should be accepted. Our method extends the traditional trust region approach by combining a filter technique into the rules for accepting trial steps so that a trial step could still be accepted even when it is rejected by the traditional rule based on merit function reduction. An estimate of the Lagrange multiplier is updated at each iteration, and the penalty parameter is updated to force sufficient reduction in the norm of the constraint violations. Active set technique is used to handle the inequality constraints. Numerical results for a set of constrained problems from the CUTEr collection are also reported.

Iterative Methods of Richardson-Lucy-Type for Image Deblurring

Image deconvolution problems with a symmetric point-spread function arisein many areas of science and engineering. These problems often are solved by theRichardson-Lucy method, a nonlinear iterative method. We first show a convergenceresult for the Richardson-Lucy method. The proof sheds light on why the method mayconverge slowly. Subsequently, we describe an iterative active set method that imposesthe same constraints on the computed solution as the Richardson-Lucy method. Computed examples show the latter method to yield better restorations than the RichardsonLucy method and typically require less computational effort.

Maximum-likelihood detection based on branch and bound algorithm for MIMO systems

Maximum likelihood detection for MIMO systems can be formulated as an integer quadratic programming problem. In this paper, we introduce depth-first branch and bound algorithm with variable dichotomy into MIMO detection. More nodes may be pruned with this structure. At each stage of the branch and bound algorithm, active set algorithm is adopted to solve the dual subproblem. In order to reduce the complexity further, the Cholesky factorization update is presented to solve the linear system at each iteration of active set algorithm efficiently. By relaxing the pruning conditions, we also present the quasi branch and bound algorithm which implements a good tradeoff between performance and complexity. Numerical results show that the complexity of MIMO detection based on branch and bound algorithm is very low, especially in low SNR and large constellations.

Aerodynamic Characteristics and Noise Collaborative Optimization of an Airfoil

Aerodynamic noise is the main problem restricting its development nowadays in green energy,ocean engineering and aerospace engineering.In order to limit the aerodynamic noise of an airfoil structure,a method is proposed in this paper by designing low noise airfoils.This method optimized the aerodynamic noise of two-dimensional airfoil,and considered the aerodynamic performance of the airfoil at the same time.Based on Joukowski conformal transformation,airfoil geometry is parameterized firstly.Then,the optimization model taking the lift-to-drag ratio and airfoil self-noise as the design objective,is established to modify the airfoil by active set algorithm until the airfoil can satisfy the design condition.Finally,the noise of the optimized airfoil is verified according to the prediction theory of airfoil noise.Moreover,the relationship between airfoil geometry and noise is analyzed.The results show that the lift-to-drag ratio of the optimized airfoil increased,and the noise also decreased.Thus,the optimization method can be used to address special design of low-noise airfoil.Besides,the optimization method in this paper can provide reference for improving lift-to-drag ratio and reducing noise of the airfoil in aircraft and submarine rudder system.

Implementation of Dynamic Matrix Control on Field Programmable Gate Array

High performance computer is often required by model predictive control(MPC) systems due to the heavy online computation burden.To extend MPC to more application cases with low-cost computation facilities, the implementation of MPC controller on field programmable gate array(FPGA) system is studied.For the dynamic matrix control(DMC) algorithm,the main design idea and the implemental strategy of DMC controller are introduced based on a FPGA’s embedded system.The performance tests show that both the computation efficiency and the accuracy of the proposed controller can be satisfied due to the parallel computing capability of FPGA.

Truncated L1 Regularized Linear Regression:Theory and Algorithm

Truncated L1 regularization proposed by Fan in[5],is an approximation to the L0 regularization in high-dimensional sparse models.In this work,we prove the non-asymptotic error bound for the global optimal solution to the truncated L1 regularized linear regression problem and study the support recovery property.Moreover,a primal dual active set algorithm(PDAS)for variable estimation and selection is proposed.Coupled with continuation by a warm-start strategy leads to a primal dual active set with continuation algorithm(PDASC).Data-driven parameter selection rules such as cross validation,BIC or voting method can be applied to select a proper regularization parameter.The application of the proposed method is demonstrated by applying it to simulation data and a breast cancer gene expression data set(bcTCGA).