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Domain-Driven Solver (DDS) Version 2.1: a MATLAB-based software package for convex optimization problems in domain-driven form
Domain-Driven Solver (DDS) is a MATLAB-based software package for convex optimization. The current version of DDS accepts every combination of the...
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Analogs of the Pólya–Szegő and Makai Inequalities for the Euclidean Moment of Inertia of a Convex Domain
In this paper, we obtain two-sided estimates for the Euclidean moment of inertia I 2 ( G ) of a convex domain G on the plane in terms of geometric...
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Two-Sided Estimate for the Torsional Rigidity of Convex Domain Generalizing the Polya–Szegö and Makai Inequalities
AbstractWe establish generalizations of the classical Polya–Szegö and Makai inequalities which estimate the torsional rigidity of a convex domain....
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Asymptotics of the Solution of a Bisingular Optimal Distributed Control Problem in a Convex Domain with a Small Parameter Multiplying a Highest Derivative
AbstractWe consider an optimal distributed control problem in a strictly convex planar domain with a smooth boundary and a small parameter...
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Mean Convex Smoothing of Mean Convex Cones
We show that any minimizing hypercone can be perturbed into one side to a properly embedded smooth minimizing hypersurface in the Euclidean space,...
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Scattering for 3D Cubic Focusing NLS on the Domain Outside a Convex Obstacle Revisited
In this article, we consider the focusing cubic nonlinear Schrödinger equation(NLS) in the exterior domain outside of a convex obstacle in ℝ 3 with...
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Log-domain interior-point methods for convex quadratic programming
Applying an interior-point method to the central-path conditions is a widely used approach for solving quadratic programs. Reformulating these...
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From valuations on convex bodies to convex functions
A geometric framework relating valuations on convex bodies to valuations on convex functions is introduced. It is shown that a classical result by...
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Convex Non-convex Variational Models
An important class of computational techniques to solve inverse problems in image processing relies on a variational approach: the optimal output is...
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Lipschitz-continuity of Spherically Convex Functions
In this article, some basic and important properties of spherically convex functions, such as the Lipschitz-continuity, are investigated. It is shown...
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Convex Functions
This chapter is devoted to convex functions, the rock star of optimization theory. In this section, we recall their key properties that matter for...
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Convex Optimization
Convex optimization or convex programming refers to the problem of minimizing convex functions over convex sets. Observe that we have been careful to...
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Relationships Between Polyhedral Convex Sets and Generalized Polyhedral Convex Sets
In this paper, we study some relationships between polyhedral convex sets and generalized polyhedral convex sets. In particular, we clarify by a...
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An online convex optimization-based framework for convex bilevel optimization
We propose a new framework for solving the convex bilevel optimization problem, where one optimizes a convex objective over the optimal solutions of...
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Packing convex polygons in minimum-perimeter convex hulls
The problem of packing a given set of freely translated and rotated convex polygons in a minimum-perimeter convex polygon (in particular the...
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Convex Generalized Differentiation
This chapter is devoted to basic constructions of convex generalized differentiation. Using the separation theorems and the intersection rule for...
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Sharp bounds on the third Hankel determinant for the Ozaki close-to-convex and convex functions
Our main purpose in this paper is to obtain certain sharp estimates of the third Hankel determinant for the class ℱ of Ozaki close-to-convex...
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Convex Analysis on Hadamard Spaces and Scaling Problems
In this paper, we address the bounded/unbounded determination of geodesically convex optimization on Hadamard spaces. In Euclidean convex...
