9,577 research outputs found
A unified approach to complementarity in optimization
AbstractAn underlying general structure of complementary pivot theory is presented with applications to various problems in optimization theory. The applications include linear complementarity, fixed point theory, unconstrained and constrained convex optimization without derivatives, nonlinear complementarity, and saddle point problems
Contact-Implicit Trajectory Optimization using an Analytically Solvable Contact Model for Locomotion on Variable Ground
This paper presents a novel contact-implicit trajectory optimization method
using an analytically solvable contact model to enable planning of interactions
with hard, soft, and slippery environments. Specifically, we propose a novel
contact model that can be computed in closed-form, satisfies friction cone
constraints and can be embedded into direct trajectory optimization frameworks
without complementarity constraints. The closed-form solution decouples the
computation of the contact forces from other actuation forces and this property
is used to formulate a minimal direct optimization problem expressed with
configuration variables only. Our simulation study demonstrates the advantages
over the rigid contact model and a trajectory optimization approach based on
complementarity constraints. The proposed model enables physics-based
optimization for a wide range of interactions with hard, slippery, and soft
grounds in a unified manner expressed by two parameters only. By computing
trotting and jumping motions for a quadruped robot, the proposed optimization
demonstrates the versatility for multi-contact motion planning on surfaces with
different physical properties.Comment: in IEEE Robotics and Automation Letter
Genetic Transfer or Population Diversification? Deciphering the Secret Ingredients of Evolutionary Multitask Optimization
Evolutionary multitasking has recently emerged as a novel paradigm that
enables the similarities and/or latent complementarities (if present) between
distinct optimization tasks to be exploited in an autonomous manner simply by
solving them together with a unified solution representation scheme. An
important matter underpinning future algorithmic advancements is to develop a
better understanding of the driving force behind successful multitask
problem-solving. In this regard, two (seemingly disparate) ideas have been put
forward, namely, (a) implicit genetic transfer as the key ingredient
facilitating the exchange of high-quality genetic material across tasks, and
(b) population diversification resulting in effective global search of the
unified search space encompassing all tasks. In this paper, we present some
empirical results that provide a clearer picture of the relationship between
the two aforementioned propositions. For the numerical experiments we make use
of Sudoku puzzles as case studies, mainly because of their feature that
outwardly unlike puzzle statements can often have nearly identical final
solutions. The experiments reveal that while on many occasions genetic transfer
and population diversity may be viewed as two sides of the same coin, the wider
implication of genetic transfer, as shall be shown herein, captures the true
essence of evolutionary multitasking to the fullest.Comment: 7 pages, 6 figure
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