We consider a class of robust optimization problems that we call "robust-to-dynamics optimization" (RDO). The input to an RDO problem is twofold: (i) a mathematical program (e.g., an LP, SDP, IP, etc.), and ...
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ISBN:
(纸本)9781479978878
We consider a class of robust optimization problems that we call "robust-to-dynamics optimization" (RDO). The input to an RDO problem is twofold: (i) a mathematical program (e.g., an LP, SDP, IP, etc.), and (ii) a dynamical system (e.g., a linear, nonlinear, discrete, or continuous dynamics). The objective is to maximize over the set of initial conditions that forever remain feasible under the dynamics. The focus of this paper is on the case where the optimization problem is a linear program and the dynamics are linear. We establish some structural properties of the feasible set and prove that if the linear system is asymptotically stable, then the RDO problem can be solved in polynomial time. We also outline a semidefinite programming based algorithm for providing upper bounds on robust-to-dynamics linear programs.
Sum of squares (SOS) optimization has been a powerful and influential addition to the theory of optimization in the past decade. Its reliance on relatively large-scale semidefinite programming, however, has seriously ...
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Sum of squares (SOS) optimization has been a powerful and influential addition to the theory of optimization in the past decade. Its reliance on relatively large-scale semidefinite programming, however, has seriously challenged its ability to scale in many practical applications. In this paper, we introduce DSOS and SDSOS optimization as more tractable alternatives to sum of squares optimization that rely instead on linear programming and second order cone programming. These are optimization problems over certain subsets of sum of squares polynomials and positive semidefinite matrices and can be of potential interest in general applications of semidefinite programming where scalability is a limitation.
In this paper we are presenting a brief overview of research on blending splines from 2004-2015. We discuss some of the properties which can be interesting to investigate when blending splines are used both for finite...
In this paper we are presenting a brief overview of research on blending splines from 2004-2015. We discuss some of the properties which can be interesting to investigate when blending splines are used both for finite element analysis and geometry. Blending splines are constructions where local geometry is blended together by a blending function to create global geometry. The different basis functions has different properties, which can be related to different application areas. Example application areas where blending splines are utilized is listed, together with a focus on the basis and future work towards utilizing parts of blending splines in an isogeometric analysis(IGA) context.
High throughput biomaterials screening largely remains unexplored. The present study was an attempt to explore the area of high throughput as well as high content screening of cell surface topographic interaction. An ...
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ISBN:
(纸本)9781618390622
High throughput biomaterials screening largely remains unexplored. The present study was an attempt to explore the area of high throughput as well as high content screening of cell surface topographic interaction. An array of surface topographies called TopoChip was fabricated using a widely used polymer in tissue engineering, Poly (DL-lactic acid). The topographies were subsequently screened for their mitogenic effect on cells. We were able to detect topographic parameters responsible for mitogenic effect of surface topographies.
In this paper we define a many-valued semantics for hybrid logic and we give a sound and complete tableau system which is proof-theoretically well-behaved, in particular, it gives rise to a decision procedure for the ...
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As concurrent software systems become larger, the interaction of their components is becoming more complex. This interaction may limit reuse, making it difficult to validate design and correctness and perhaps forcing ...
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ISBN:
(纸本)0769510809
As concurrent software systems become larger, the interaction of their components is becoming more complex. This interaction may limit reuse, making it difficult to validate design and correctness and perhaps forcing reengineering of these systems in order to meet future requirements. In order to reduce this complexity and to build stable and adaptable concurrent software systems, we present an approach that emphasizes the separation of interaction components from the functional components.
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