Polynomial optimization considers optimization problems defined by polynomials. In contrast to classical nonlinearoptimization, it aims at finding global optimizers. Tensors are natural higher-order generalizations of matrices and are closely related to polynomials and moments. They are powerful tools in studying tensors. Many tensor problems can be formulated as polynomial optimization problems.

We propose a complete semidefinite relaxation algorithmfor detecting the copositivity of a symmetric tensor. We show that the detection can be done by solving a finite number of semidefinite relaxations for all tensors.

For the saddle point problem of polynomials,we give an algorithm for computing saddle points. We show that: i) if there exists a saddle point, our algorithm can get one by solving a finite number of Lasserre type semidefinite relaxations; ii) if there is no saddle point, our algorithm can detect its nonexistence.

Hermitian tensors are generalizations of Hermitian matrices, but they have very different properties. Canonical basis Hermitian tensors, real Hermitian tensors, special matrix flattenings, positive semidefiniteness, and separability are studied. We further study how to detect separability of Hermitian tensors. We formulate this as a truncated moment problem and then provide a semidefinite relaxation algorithm to solve it.

The problem of learning diagonal Gaussian mixture models can be formulated as computing incomplete symmetric tensor decompositions. We use generating polynomials to compute incomplete symmetric tensor decompositions and approximations. Then the tensor approximation is used to learn diagonal Gaussian mixture models. When the first and third order moments are sufficiently accurate, we show that the obtained parameters for the Gaussian mixture models are also highly accurate.

My dissertation explores the ways the media industries of the Chinese Nationalist Party turned Taiwan and Hong Kong—the Nationalist’s industrial home-front and informational hub—into what I call a regime of logistics after 1949. As one of the greatest human migrations in modern history, the mass exodus of millions of Chinese people to Taiwan and Hong Kong upon the triumph of the Communist party has been relatively understudied. The movement of military personnel, intellectuals, technocrats, and business communities represented a singular mode of migratory culture, as they were not only victims displaced by the Chinese Civil War but also a powerful cluster of human resources with which the Nationalist regime engineered the image of a “Free China” with the support from the United States. In this context, I ask how military, industrial, and commercial logistics forged a propaganda media infrastructure that both circulated and represented the movement of labor, information, and affects in the supply-chain capitalism during the Cold War.

My dissertation inquiries into the specific ways state-sponsored cinema and literature turned the narratives of displacement into narratives defined by postwar developmentalism. It is my contention that in the process of being relocated and downscaled from a continental sovereignty to an exiled island-state, the Nationalists’ pursuit of a techno-utopia forged a series of media environments from which new cinematic and literary aesthetics emerged within the intertwined milieu between warfare and development. How did Taiwan and Hong Kong reshape the Nationalists’ narratives of nation-building and military logistics with their own aesthetic strategies? What do these strategies tell us about the relations among militarism, migration, and environment? To map out the interconnected conduits of aesthetic transformation between propaganda discourses and creative freedom, I read audiovisual images and literary texts against four principal enterprises for Nationalists’ mobilization—military science, agricultural campaigns, transportation networks, and architectural planning. Each of these medium/environment clusters is centered around a state-run enterprise—transplanted from China to either Taiwan or Hong Kong—and its correlated technocratic discourses. In aggregate, these images and texts provide the basis for a new narrative of Taiwan and Hong Kong’s Cold War culture.