A new polynomial-time algorithm for linear programming
Combinatorica
Mathematical Programming: Series A and B
Evaluating derivatives: principles and techniques of algorithmic differentiation
Evaluating derivatives: principles and techniques of algorithmic differentiation
Shapes and geometries: analysis, differential calculus, and optimization
Shapes and geometries: analysis, differential calculus, and optimization
Interior Methods for Nonlinear Optimization
SIAM Review
An Interior Point Algorithm for Large-Scale Nonlinear Programming
SIAM Journal on Optimization
Path-following Methods for a Class of Constrained Minimization Problems in Function Space
SIAM Journal on Optimization
Numerical Simulation of Acoustic Streaming on Surface Acoustic Wave-driven Biochips
SIAM Journal on Scientific Computing
Primal-dual interior-point methods for PDE-constrained optimization
Mathematical Programming: Series A and B
Path-following methods for shape optimal design of periodic microstructural materials
Optimization Methods & Software - THE JOINT EUROPT-OMS CONFERENCE ON OPTIMIZATION, 4-7 JULY, 2007, PRAGUE, CZECH REPUBLIC, PART II
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The paper deals with applications of numerical methods for optimal shape design of composite materials structures and devices. We consider two different physical models described by specific partial differential equations (PDEs) for real-life problems. The first application relates microstructural biomorphic ceramic materials for which the homogenization approach is invoked to formulate the macroscopic problem. The obtained homogenized equation in the macroscale domain is involved as an equality constraint in the optimization task. The second application is connected to active microfluidic biochips based on piezoelectrically actuated surface acoustic waves (SAWs). Our purpose is to find the best material-and-shape combination in order to achieve the optimal performance of the materials structures and, respectively, an improved design of the novel nanotechnological devices. In general, the PDEs constrained optimization routine gives rise to a large-scale nonlinear programming problem. For the numerical solution of this problem we use one-shot methods with proper optimization algorithms and inexact Newton solvers. Computational results for both applications are presented and discussed.