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.

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.

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).

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.