Results 1 to 10 of about 322,181 (169)
Inverse polynomial optimization [PDF]
IEEE Conference on Decision and Control and European Control Conference, 2012 We consider the inverse optimization problem associated with the polynomial program f^*=\min \{f(x): x\in K\}$ and a given current feasible solution $y\in K$. We provide a systematic numerical scheme to compute an inverse optimal solution.
Lasserre, Jean-Bernard
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An Elementary Approach to Polynomial Optimization on Polynomial Meshes
Journal of Mathematical and Fundamental Sciences, 2018 A polynomial mesh on a multivariate compact set or manifold is a sequence of finite norming sets for polynomials whose norming constant is independent of degree.
Marco Vianello
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Optimal Domination Polynomials [PDF]
Graphs and Combinatorics, 2020 Let $G$ be a graph on $n$ vertices and $m$ edges and $D(G,x)$ the domination polynomial of $G$. In this paper we completely characterize the values of $n$ and $m$ for which optimal graphs exist for domination polynomials. We also show that there does not always exist least optimal graphs for the domination polynomial.
Iain Beaton +2 more
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Optimization Over Trace Polynomials [PDF]
Annales Henri Poincaré, 2021 Motivated by recent progress in quantum information theory, this article aims at optimizing trace polynomials, i.e., polynomials in noncommuting variables and traces of their products. A novel Positivstellensatz certifying positivity of trace polynomials subject to trace constraints is presented, and a hierarchy of semidefinite relaxations converging ...
Klep, Igor +2 more
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Mathematics, 2022 In this paper, we discuss the cone of copositive tensors and its approximation. We describe some basic properties of copositive tensors and positive semidefinite tensors. Specifically, we show that a non-positive tensor (or Z-tensor) is copositive if and
Muhammad Faisal Iqbal, Faizan Ahmed
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The Non-Tightness of a Convex Relaxation to Rotation Recovery
Sensors, 2021 We study the Perspective-n-Point (PNP) problem, which is fundamental in 3D vision, for the recovery of camera translation and rotation. A common solution applies polynomial sum-of-squares (SOS) relaxation techniques via semidefinite programming. Our main
Yuval Alfassi +2 more
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Stochastic polynomial optimization [PDF]
Optimization Methods and Software, 2019 This paper studies stochastic optimization problems with polynomials. We propose an optimization model with sample averages and perturbations. The Lasserre type Moment-SOS relaxations are used to solve the sample average optimization. Properties of the optimization and its relaxations are studied. Numerical experiments are presented.
Nie, Jiawang, Yang, Liu, Zhong, Suhan
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A Fast and Reliable Solution to PnP, Using Polynomial Homogeneity and a Theorem of Hilbert
Sensors, 2023 One of the most-extensively studied problems in three-dimensional Computer Vision is “Perspective-n-Point” (PnP), which concerns estimating the pose of a calibrated camera, given a set of 3D points in the world and their corresponding 2D projections in ...
Daniel Keren +2 more
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CPD-Structured Multivariate Polynomial Optimization
Frontiers in Applied Mathematics and Statistics, 2022 We introduce the Tensor-Based Multivariate Optimization (TeMPO) framework for use in nonlinear optimization problems commonly encountered in signal processing, machine learning, and artificial intelligence.
Muzaffer Ayvaz +3 more
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Grover Adaptive Search for Constrained Polynomial Binary Optimization [PDF]
Quantum, 2021 In this paper we discuss Grover Adaptive Search (GAS) for Constrained Polynomial Binary Optimization (CPBO) problems, and in particular, Quadratic Unconstrained Binary Optimization (QUBO) problems, as a special case.
Austin Gilliam +2 more
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