scholarly journals The Non-Tightness of a Convex Relaxation to Rotation Recovery

Sensors ◽  
2021 ◽  
Vol 21 (21) ◽  
pp. 7358
Author(s):  
Yuval Alfassi ◽  
Daniel Keren ◽  
Bruce Reznick
Keyword(s):  
Algebraic Geometry ◽  
Polynomial Optimization ◽  
Convex Relaxation ◽  
Real Life ◽  
Probability Of Failure ◽  
Relaxation Techniques ◽  
3D Vision ◽  
Theoretical Contribution ◽  
Common Solution ◽  
Lasserre Hierarchy

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 result is that the polynomials which should be optimized can be non-negative but not SOS, hence the resulting convex relaxation is not tight; specifically, we present an example of real-life configurations for which the convex relaxation in the Lasserre Hierarchy fails, in both the second and third levels. In addition to the theoretical contribution, the conclusion for practitioners is that this commonly-used approach can fail; our experiments suggest that using higher levels of the Lasserre Hierarchy reduces the probability of failure. The methods we use are mostly drawn from the area of polynomial optimization and convex relaxation; we also use some results from real algebraic geometry, as well as Matlab optimization packages for PNP.

scholarly journals Hierarchical Fusion of Machine Learning Algorithms in Indoor Positioning and Localization

2019 ◽  
Vol 9 (18) ◽  
pp. 3665 ◽  
Author(s):  
Ahmet Çağdaş Seçkin ◽  
Aysun Coşkun
Keyword(s):  
Machine Learning ◽  
Performance Metrics ◽  
Deductive Reasoning ◽  
Real Life ◽  
Indoor Positioning ◽  
Machine Learning Algorithms ◽  
Learning Models ◽  
Positioning Systems ◽  
Common Solution ◽  
Variable Reduction

Wi-Fi-based indoor positioning offers significant opportunities for numerous applications. Examining the Wi-Fi positioning systems, it was observed that hundreds of variables were used even when variable reduction was applied. This reveals a structure that is difficult to repeat and is far from producing a common solution for real-life applications. It aims to create a common and standardized dataset for indoor positioning and localization and present a system that can perform estimations using this dataset. To that end, machine learning (ML) methods are compared and the results of successful methods with hierarchical inclusion are then investigated. Further, new features are generated according to the measurement point obtained from the dataset. Subsequently, learning models are selected according to the performance metrics for the estimation of location and position. These learning models are then fused hierarchically using deductive reasoning. Using the proposed method, estimation of location and position has proved to be more successful by using fewer variables than the current studies. This paper, thus, identifies a lack of applicability present in the research community and solves it using the proposed method. It suggests that the proposed method results in a significant improvement for the estimation of floor and longitude.

Convex underestimating relaxation techniques for nonconvex polynomial programming problems: computational overview

2015 ◽  
Vol 24 (3-4) ◽  
pp. 129-143
Author(s):  
André A. Keller
Keyword(s):  
System Analysis ◽  
Convex Set ◽  
Optimization Problems ◽  
Convex Relaxation ◽  
Engineering Application ◽  
Global Optimum ◽  
Linear Matrix ◽  
Quadratic Term ◽  
Relaxation Techniques ◽  
Convex Envelopes

AbstractThis paper introduces constructing convex-relaxed programs for nonconvex optimization problems. Branch-and-bound algorithms are convex-relaxation-based techniques. The convex envelopes are important, as they represent the uniformly best convex underestimators for nonconvex polynomials over some region. The reformulation-linearization technique (RLT) generates linear programming (LP) relaxations of a quadratic problem. RLT operates in two steps: a reformulation step and a linearization (or convexification) step. In the reformulation phase, the constraint and bound inequalities are replaced by new numerous pairwise products of the constraints. In the linearization phase, each distinct quadratic term is replaced by a single new RLT variable. This RLT process produces an LP relaxation. The LP-RLT yieds a lower bound on the global minimum. LMI formulations (linear matrix inequalities) have been proposed to treat efficiently with nonconvex sets. An LMI is equivalent to a system of polynomial inequalities. A semialgebraic convex set describes the system. The feasible sets are spectrahedra with curved faces, contrary to the LP case with polyhedra. Successive LMI relaxations of increasing size yield the global optimum. Nonlinear inequalities are converted to an LMI form using Schur complements. Optimizing a nonconvex polynomial is equivalent to the LP over a convex set. Engineering application interests include system analysis, control theory, combinatorial optimization, statistics, and structural design optimization.

scholarly journals Towards a Comprehensive Understanding of Fertility: The Model of Dyadic Pathways

2019 ◽  
Vol 44 ◽  
Author(s):  
Uta Brehm ◽  
Norbert F. Schneider
Keyword(s):  
Theory Of Planned Behaviour ◽  
Research Question ◽  
Real Life ◽  
The Body ◽  
Theoretical Contribution ◽  
Future Fertility ◽  
Self Reports ◽  
Individual Self ◽  
The Impact ◽  
Relevant Factors

In this theoretical contribution, we propose a comprehensive and integrative heuristic model to explain fertility, the Model of Dyadic Pathways (MDP). We show how existing models such as the Theory of Planned Behaviour often do not withstand empirical challenges, especially not individual self-reports in qualitative studies. Furthermore, existing models vary in their premises and foci, resulting in a collection of models which do not necessarily align with or supplement one another. For these reasons, these heuristic models have been widely criticised and, in practice, pieced together according to the research question and tradition of the researcher. Against this backdrop, we establish the MDP to reconnect theory with reality and to unify a variety of approaches. The MDP is grounded on the dyad of partners as the prevalent basis of fertility. It integrates reasoned and unreasoned fertility behaviour, the impact of individual- and couple-level life course, soci(et)al conditions, and the body as an “actor”. The model explicitly accounts for the variety of different real-life pathways that lead to fertility. It thereby encourages researchers to, first, consider all potentially relevant factors and their mechanisms and, second, think of fertility and its measurement as a multilinear process. Based on the presented elements a comprehensive model of fertility must cover, we suggest ways to improve surveys accordingly. Furthermore, we elaborate on the contributions and challenges the MDP presents to future fertility research.

The process by which executives unlearn their attachments in order to facilitate change

2019 ◽  
Vol 39 (2) ◽  
pp. 145-164
Author(s):  
Rene Rautenbach ◽  
Margie Sutherland ◽  
Caren B Scheepers
Keyword(s):  
Qualitative Research ◽  
Literature Review ◽  
Empirical Research ◽  
Process Model ◽  
Life Experiences ◽  
Real Life ◽  
Theoretical Contribution ◽  
New Concepts ◽  
Depth Interviews ◽  
Attachment Behaviour

Unlearning an attachment has become a critical change competence for executives. Although attachment behaviour in the workplace is ubiquitous, there is a scarcity of empirical research on the processes executives follow in order to release their dysfunctional attachments to systems, routines, ideas, divisions and certain members of staff. By unlearning attachments, executives can embrace new concepts, methods and processes and thereby enable their organisations to be more competitive. This qualitative research investigated executives’ experiences of unlearning an attachment, through the pre-unlearning, unlearning and post-unlearning phases. A de jure model was formulated from concepts that emerged during the literature review and this model was the basis of in-depth interviews with 10 change experts and 10 executives who had unlearned attachments. The executives and change experts shared real-life experiences during each of the unlearning phases. The findings informed a de facto model of the experiences of executives unlearning their attachments. This process model makes a theoretical contribution by depicting the major types of attachments, influences on, processes of, actions required by and outcome of the executives’ unlearning. The model should contribute to change practitioners’ facilitation of executives’ unlearning processes and executives’ insights into their own attachments.

scholarly journals Nonlinear Algebra and Applications

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Paul Breiding ◽  
Türkü Özlüm Çelik ◽  
Timothy Duff ◽  
Alexander Heaton ◽  
Aida Maraj ◽  
...  
Keyword(s):  
Algebraic Geometry ◽  
Partial Differential Equations ◽  
Integrable Systems ◽  
Polynomial Optimization ◽  
Configuration Spaces ◽  
Reaction Networks ◽  
Algebraic Statistics ◽  
Biochemical Reaction Networks ◽  
Tensor Decompositions ◽  
Nonlinear Algebra

<p style='text-indent:20px;'>We showcase applications of nonlinear algebra in the sciences and engineering. Our review is organized into eight themes: polynomial optimization, partial differential equations, algebraic statistics, integrable systems, configuration spaces of frameworks, biochemical reaction networks, algebraic vision, and tensor decompositions. Conversely, developments on these topics inspire new questions and algorithms for algebraic geometry.</p>

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