We propose an extension of Newton’s Method for unconstrained multiobjective optimization (multicriteria optimization). The method does not scalarize the original vector optimization problem, i.e. we do not make use of any of the classical techniques that transform a multiobjective problem into a family of standard optimization problems. Neither ordering information nor weighting factors for the...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 19 February 2021Accepted: 27 August 2021Published online: 04 January 2022Keywordsoptimal transport, linear embeddings, Hellinger--Kantorovich Distance, exponential and logarithmic mapsAMS Subject Headings49M30, 49K20, 49N90Publication DataISSN (online): 1936-4954Publisher...

In this paper, we are interested in the time derivative of the Wasserstein distance between the marginals of two Markov processes. As recalled in the introduction, the Kantorovich duality leads to a natural candidate for this derivative. Up to the sign, it is the sum of the integrals with respect to each of the two marginals of the corresponding generator applied to the corresponding Kantorovic...

We develop a full theory for the new class of Optimal Entropy-Transport problems between nonnegative and finite Radon measures in general topological spaces. They arise quite naturally by relaxing the marginal constraints typical of Optimal Transport problems: given a couple of finite measures (with possibly different total mass), one looks for minimizers of the sum of a linear transport functi...

In this talk, we introduce a rigorous computational method for proving existence of periodic orbits of continuous and discontinuous (Filippov) piecewise-smooth differential equations. The computer-assisted proofs are obtained by combining a functional analytic approach based on Chebyshev series together with a Newton-Kantorovich type argument (the radii polynomial approach). Using this approach...

This paper presents a numerical implementation of inverse and direct kinematics of a 3-DOF parallel robot with R-P-S (Revolute-Prismatic-Spherical) joint structure using Matlab. The robot has two degrees of orientation freedom and one degree of translatory freedom. The inverse kinematics was expressed in term of Z-Y-Z Euler angles and direct kinematics was solved numerically using Newton-Kantor...

One revisits the standard saddle-point method based on conjugate duality for solving convex minimization problems. Our aim is to reduce or remove unnecessary topological restrictions on the constraint set. Dual equalities and characterizations of the minimizers are obtained with weak or without constraint qualifications. The main idea is to work with intrinsic topologies which reflect some geom...

the cracked brazilian disc (cbd) specimen is widely used in order to determine mode-i/ii and mixed-mode fracture toughness of a rock medium. in this study, the stress intensity factor (sif) on the crack-tip in this specimen is calculated for various geometrical crack conditions using the extended-finite element method (x-fem). this method is based upon the finite element method (fem). in this m...