相关论文: Hierarchy of bounds in free orthotropic material o…

Topology optimization of frame structures under free-vibration eigenvalue constraints constitutes a challenging nonconvex polynomial optimization problem with disconnected feasible sets. In this article, we first formulate it as a…

This paper presents an efficient algorithm for the approximation of the rank-one convex hull in the context of nonlinear solid mechanics. It is based on hierarchical rank-one sequences and simultaneously provides first and second derivative…

The paper establishes exact lower bound on the effective elastic energy of two-dimensional, three-material composite subjected to the homogeneous, anisotropic stress. It is assumed that the materials are mixed with given volume fractions…

In this article, a compliance minimisation scheme for designing spatially varying orthotropic porous structures is proposed. With the utilisation of conformal mapping, the porous structures here can be generated by two controlling field…

We formalise decompression planning as an optimal control problem with gas feasibility windows (ppO$_2$, END), affine ceilings, and convex penalties in normalised oversaturation. The depth trajectory is constrained to be a monotone ascent,…

Weight optimization of frame structures with continuous cross-section parametrization is a challenging non-convex problem that has traditionally been solved by local optimization techniques. Here, we exploit its inherent semi-algebraic…

In this paper we investigate numerically an instance of the problem of G-closure for two-dimensional periodic metamaterials. Specifically, we consider composites with isotropic homogenized elasticity tensor, obtained as a mixture of two…

In this paper, we propose a new convergent conic programming hierarchy of relaxations involving both semi-definite cone and second-order cone constraints for solving nonconvex polynomial optimization problems to global optimality. The…

We consider the minimization of a continuous function over the intersection of a regular cone with an affine set via a new class of adaptive first- and second-order optimization methods, building on the Hessian-barrier techniques introduced…

The relaxation in the calculus of variation motivates the numerical analysis of a class of degenerate convex minimization problems with non-strictly convex energy densities with some convexity control and two-sided $p$-growth. The…

The paper establishes tight lower bound for effective conductivity tensor $K_*$ of two-dimensional three-phase conducting anisotropic composites and defines optimal microstructures. It is assumed that three materials are mixed with fixed…

This paper considers stochastic convex optimization problems with smooth functional constraints arising in constrained estimation and robust signal recovery. We operate in the high-dimensional and highly-constrained setting, where oracle…

This thesis explores algorithmic applications and limitations of convex relaxation hierarchies for approximating some discrete and continuous optimization problems. - We show a dichotomy of approximability of constraint satisfaction…

This paper proposes two convergent adaptive mesh-refining algorithms for the hybrid high-order method in convex minimization problems with two-sided p-growth. Examples include the p-Laplacian, an optimal design problem in topology…

We propose an approach to trajectory optimization for piecewise polynomial systems based on the recently proposed graphs of convex sets framework. We instantiate the framework with a convex relaxation of optimal control based on occupation…

This paper studies the hierarchy of sparse matrix Moment-SOS relaxations for solving sparse polynomial optimization problems with matrix constraints. First, we prove a sufficient and necessary condition for the sparse hierarchy to be tight.…

Constrained second-order convex optimization algorithms are the method of choice when a high accuracy solution to a problem is needed, due to their local quadratic convergence. These algorithms require the solution of a constrained…

Convex relaxation methods are powerful tools for studying the lowest energy of many-body problems. By relaxing the representability conditions for marginals to a set of local constraints, along with a global semidefinite constraint, a…

This paper develops a robust fixed time optimization framework for constrained problems that guarantees exact constraint satisfaction and convergence to KKT points within fixed time , independent of initial conditions. The approach treats…

When discretizing symmetric stress tensors in variational problems arising in continuum mechanics, one has to choose how to enforce the symmetry of the stress tensor: (i) strongly by requiring the discrete tensors to be pointwise symmetric…