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Scalable enforcement of geometric non-interference constraints for gradient-based optimization
Many design optimization problems include constraints to prevent intersection of the geometric shape being optimized with other objects or with...
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Polynomial Optimization in Geometric Modeling
In this chapter, we review applications of Polynomial Optimization techniques to Geometric Modeling problems. We present examples of topical problems...
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A neurodynamic approach for joint chance constrained rectangular geometric optimization
This paper considers a nonconvex geometric optimization problem with two-sided joint probabilistic constraints, namely rectangular constraints. We...
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Extremal Geometric Measure of Entanglement and Riemannian Optimization Methods
In this paper, we study the extremal geometric measure of quantum entanglement of superposition states of several symmetric pure states with...
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Geometric Aspects of Shape Optimization
We present a review of known results in shape optimization from the point of view of Geometric Analysis. This paper is devoted to the mathematical...
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Geometric Constrained Scalable Algorithm for PDE-Constrained Shape Optimization
In this project, the parallel performance of shape optimization schemes is investigated using varying core counts for several levels of refinement....
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Geometric design of electric motors using adjoint-based shape optimization
Interest in electric aircraft has increased due to developments in electric propulsion technology and concerns regarding aircraft carbon emissions....
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Inexact penalty decomposition methods for optimization problems with geometric constraints
This paper provides a theoretical and numerical investigation of a penalty decomposition scheme for the solution of optimization problems with...
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An augmented Lagrangian method for optimization problems with structured geometric constraints
This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with...
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Modeling the Movement of Heterogenous Flows of People as a Geometric Design Problem
The problem of modeling the movement of heterogenous flows of people is shown to be one of the topical applied problems of the geometric design...
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Topology optimization and geometric nonlinear modeling using positional finite elements
Topology optimization is an effective approach for the efficient layout design of structures and their components. This approach is well-established...
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Introduction to Geometric Algebra
Geometric algebra was initiated by W.K. Clifford over 140 years ago. It unifies all branches of physics, and has found rich applications in robotics,...
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A level set method for Laplacian eigenvalue optimization subject to geometric constraints
We consider to solve numerically the shape optimization problems of Dirichlet Laplace eigenvalues subject to volume and perimeter constraints. By...
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A global interior point method for nonconvex geometric programming
The strategy presented in this paper differs significantly from existing approaches as we formulate the problem as a standard optimization problem of...
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Stochastic algorithms with geometric step decay converge linearly on sharp functions
Stochastic (sub)gradient methods require step size schedule tuning to perform well in practice. Classical tuning strategies decay the step size...
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Geometric Programming Problems with Triangular and Trapezoidal Twofold Uncertainty Distributions
Geometric programming is a well-known optimization tool for dealing with a wide range of nonlinear optimization and engineering problems. In general,...
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Bregman dynamics, contact transformations and convex optimization
Recent research on accelerated gradient methods of use in optimization has demonstrated that these methods can be derived as discretizations of...
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Using Geometric Arithmetic Mean to Solve Non-linear Fractional Programming Problems
In this paper, the researchers will present geometric arithmetic mean to solve non-linear fractional programming. To do this, we shall derive the...
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Geometric Preliminaries
We assume that the reader is familiar with basic Riemannian geometryRiemannian geometrybasic definitions and we freely refer to [17] and in...