Related papers: Exploiting Lagrange duality for topology optimizat…
There are many important practical optimization problems whose feasible regions are not known to be nonempty or not, and optimizers of the objective function with the least constraint violation prefer to be found. A natural way for dealing…
In this paper we study a robust utility maximization problem in continuous time under model uncertainty. The model uncertainty is governed by a continuous semimartingale with uncertain local characteristics. Here, the differential…
Forced response curves (FRCs) of nonlinear systems can exhibit complex behaviors, including hardening/softening behavior and bifurcations. Although topology optimization holds great potential for tuning these nonlinear dynamic responses,…
This paper provides a method for the simultaneous topology optimization of parts and their corresponding joint locations in an assembly. Therein, the joint locations are not discrete and predefined, but continuously movable. The underlying…
We consider the problem of learning low-rank tensors from partial observations with structural constraints, and propose a novel factorization of such tensors, which leads to a simpler optimization problem. The resulting problem is an…
An uniform LP duality is an useful property of conic matrix systems. A consistent linear conic optimization problem yields uniform LP duality if for any linear cost function, for which the primal problem has finite optimal value, the…
Sliding cable system with frictions is encountered in many engineering applications. Such system is typically characterized by existences of complex and varied motion states of different sliding nodes (pulleys), which leads to significant…
This manuscript presents an approach for simultaneously optimizing the connectivity and elevation of grid-shell structures acting in pure compression (or pure tension) under the combined effects of a prescribed external loading and the…
Photonic topology optimization is a technique used to find the electric permittivity distribution of a device that optimizes an electromagnetic figure-of-merit. Two common techniques are used: continuous density-based optimizations that…
The problem of optimizing over random structures emerges in many areas of science and engineering, ranging from statistical physics to machine learning and artificial intelligence. For many such structures finding optimal solutions by means…
In this paper, mixed categorical structural optimization problems are investigated. The aim is to minimize the weight of a truss structure with respect to cross-section areas, materials and cross-section type. The proposed methodology…
In this paper we consider a method of solving optimal stopping problems in discrete and continuous time based on their dual representation. A novel and generic simulation-based optimization algorithm not involving nested simulations is…
In this paper, we study the Fenchel-Rockafellar duality and the Lagrange duality in the general frame work of vector spaces without topological structures. We utilize the geometric approach, inspired from its successful application by B. S.…
Canonical duality-triality is a breakthrough methodological theory, which can be used not only for modeling complex systems within a unified framework, but also for solving a wide class of challenging problems from real-world applications.…
We propose an extension of the F-maximization principle to take into account the effects of non-superconformality. Guided by a four-dimensional analog, we formulate a modification of the free energy via the Lagrange multiplier technique. We…
The revolutionary advancements in metal additive manufacturing have enabled the production of alloy-based lattice structures with complex geometrical features and high resolutions. This has encouraged the development of nonlinear material…
We establish a geometric condition guaranteeing exact copositive relaxation for the nonconvex quadratic optimization problem under two quadratic and several linear constraints, and present sufficient conditions for global optimality in…
Continuous formulations of trajectory planning problems have two main benefits. First, constraints are guaranteed to be satisfied at all times. Secondly, dynamic obstacles can be naturally considered with time. This paper introduces a novel…
Starting from a problem in elastoplasticity, we consider an optimization problem $C(c_1,c_2)=c_1+c_2\to \min$ under constraints $F_R^k(c_1,c_2)=a\cdot F^k(c_1,c_2)+b\cdot R^k(c_1,c_2)\ge 1$ and $F^k(c_1,c_2)\ge 1$, where both $F^k$ and…
Solving dynamic topology optimization problems often yields low-performing local optima. Instead of converging towards a design that exploits dynamic mechanisms, a less interesting, mass-driven solution is often generated. This necessitates…