existence and uniqueness – Optimization Online

Modelling and Analysis of an Inverse Parameter Identification Problem in Piezoelectricity

Published: 2026/02/23

Infinite Dimensional Optimization, Nonlinear Systems and Least-Squares, Systems governed by Differential Equations Optimization adjoint PDEs, existence and uniqueness, improved regularity, inverse parameter identification, operator analysis, piezoelectricity

Piezoelectric material behavior is mathematically described by coupled hyperbolic-elliptic partial differential equations (PDEs) governing mechanical displacement and electrical potential. This paper presents advancements in the theory of identifying material parameters in piezoelectric PDEs. We focus on modeling and analyzing the inverse problem assuming matrix-valued Sobolev-Bochner parameters to encompass a time and space-dependent setting and thus … Read more

Strengthened Existence and Uniqueness Conditions for Search Directions in Semidefinite Programming

Published: 2003/07/24, Updated: 2004/06/28

Levent Tunçel

Henry Wolkowicz

Convex Optimization, Semi-definite Programming existence and uniqueness, kronecker product, linear matrix equations, linear operators, semidefinite programming, symmetric kronecker product

Primal-dual interior-point (p-d i-p) methods for Semidefinite Programming (SDP) are generally based on solving a system of matrix equations for a Newton type search direction for a symmetrization of the optimality conditions. These search directions followed the derivation of similar p-d i-p methods for linear programming (LP). Among these, a computationally interesting search direction is … Read more