Using interior point solvers for optimizing progressive lens models with spherical coordinates
| Autor: | Glòria Casanellas, Jordi Castro |
|---|---|
| Přispěvatelé: | Universitat Politècnica de Catalunya. Doctorat en Estadística i Investigació Operativa, Universitat Politècnica de Catalunya. Departament d'Estadística i Investigació Operativa, Universitat Politècnica de Catalunya. GNOM - Grup d'Optimització Numèrica i Modelització |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Control and Optimization
Computer science 0211 other engineering and technologies Aerospace Engineering Optimization Industry Applications 02 engineering and technology 90 Operations research mathematical programming::90C Mathematical programming [Classificació AMS] Operations research Convexity Nonlinear programming law.invention Progressive Lenses law Applied mathematics Cartesian coordinate system Nonlinear Optimization Optical Lens Design 021108 energy Electrical and Electronic Engineering Civil and Structural Engineering computer.programming_language 021103 operations research Interior Point Methods Mechanical Engineering Optimització industrial Spherical coordinate system AMPL Lens (optics) Optical lens design computer Software Interior point method Matemàtiques i estadística::Investigació operativa::Optimització [Àrees temàtiques de la UPC] |
| Zdroj: | UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) |
| Popis: | This is a post-peer-review, pre-copyedit version of an article published in Optimization and engineering. The final authenticated version is available online at: http://dx.doi.org/10.1007/s11081-019-09480-z Designing progressive lenses is a complex problem that has been previously solved by formulating an optimization model based on Cartesian coordinates. This work presents a new progressive lens model using spherical coordinates, and interior point solvers are used to solve this new optimization model. Although this results in a highly nonlinear, nonconvex, continuous optimization problem, the new spherical coordinates model exhibits better convexity properties compared to previous ones based on Cartesian coordinates. The real-world instances considered result in nonlinear optimization problems of about 900 variables and 15,000 constraints. Each constraint corresponds to a point on the grid that defines the lens surface. The number of variables depends on the precision of the B-spline basis used for representing the surface; and the number of constraints depends on the shape and quality of the design. We present our results for progressive lenses, which were obtained using the AMPL modeling language and the nonlinear interior point solvers IPOPT, LOQO and KNITRO. The computational results are reported, as well as some examples of real-world progressive lenses that were calculated using this new model. In terms of quality, the progressive lenses obtained by our model are competitive with those of previous models used for commercial eyeglasses. |
| Databáze: | OpenAIRE |
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