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The design process of complex engineering systems may involve problems in which the number and type of design variables and constraints vary throughout the optimization process based on the values of dimensional variables. This category of problems is ...

We propose a multilevel optimization algorithm (MLO) for solving large scale instances of the Multi-Period Battery Swapping Station Location Problem (MBSSLP), i.e., a problem for deciding the placement of battery swapping stations in an urban ...

In deep learning applications, image understanding is a crucial task, where several techniques such as image captioning and visual question answering have been widely studied to improve and evaluate the performances of deep neural networks (DNN) in this ...

Large-scale optimization problems arising from the discretization of problems involving PDEs sometimes admit solutions that can be well approximated by low-rank matrices. In this paper, we will exploit this low-rank approximation property by solving the ...

Recovering a low-rank matrix from highly corrupted measurements arises in compressed sensing of structured high-dimensional signals (e.g., videos and hyperspectral images among others). Robust principal component analysis, solved via principal component ...

Cloth simulation is an important topic for many applications in computer graphics, animation, and augmented virtual reality. The mechanical behavior of cloth objects can be modeled by the Kirchhoff--Love thin shell equations, which lead to large-scale, ...

Surrogate Model Based Optimization (SMBO) is an established technique for handling computationally expensive optimization problems. One important application is the optimization of Particle Reinforced Metal Matrix Composites (PRMMCs). Multi-phase ...

Coherent risk measures have become a popular tool for incorporating risk aversion into stochastic optimization models. For dynamic models in which uncertainty is resolved at more than one stage, however, using coherent risk measures within a standard ...

Composite convex optimization models arise in several applications and are especially prevalent in inverse problems with a sparsity inducing norm and in general convex optimization with simple constraints. The most widely used algorithms for convex ...

An algorithm is developed for projecting a point onto a polyhedron. The algorithm solves a dual version of the projection problem and then uses the relationship between the primal and dual to recover the projection. The techniques in the paper exploit ...

A computationally efficient algorithm for electromagnetic EM-simulation-driven design optimization of microwave structures is proposed. Our technique exploits variable-fidelity EM simulations and the multilevel design approach where an approximate ...

A multilevel optimization approach termed MG/Opt is presented for the solution of equality-constrained optimization problems. The approach assumes that one has a hierarchy of models, ordered from fine to coarse, of an underlying optimization problem and ...

Multilevel optimization problems deals with mathematical programming problems whose feasible set is implicitly determined by a sequence of nested optimization problems. These kind of problems are common in different applications where there is a ...

Optimal design of complex engineering systems, such as aircraft composite structures, can often be accomplished only by applying decomposition techniques. In this paper, the optimal design of a composite wing-box is addressed by using a two-level scheme ...

We present optimization algorithms for the design of complex hierarchical systems, motivated by applications to the design of nanoporous materials. Nanoporous materials have a broad range of engineering applications, including gas storage and filtration, ...

This paper proposes a multilevel placer targeted at hierarchical FPGA (Field Programmable Gate Array) devices. The placer is based on multilevel optimization method which combines the multilevel bottom-up clustering process and top-down placement ...

New approximate secant equations are shown to result from the knowledge of (problem dependent) invariant subspace information, which in turn suggests improvements in quasi-Newton methods for unconstrained minimization. A new limited-memory Broyden-...

We present a trilevel optimization model of resource allocation in electric power network defense. This model identifies the most critical network components to defend against possible terrorist attacks. The goal of defense is to minimize the economic ...

To handle modern routing with nanometer effects, we need to consider designs with variable wire/via widths and spacings, for which gridless-routing approaches are desirable due to its great flexibility. In this paper, we introduce a gridless-routing ...