The paracatadioptric camera is one of the most popular panoramic systems currently available in the market. It provides a wide field of view by combining a parabolic shaped mirror with a camera inducing an orthographic projection. Previous work proved that the paracatadioptric projection of a line is a conic curve, and that the sensor can be fully calibrated from the image of three or more line...

NIE, TIANTIAN. Quadratic Programming with Discrete Variables. (Under the direction of Dr. Shu-Cherng Fang.) In this dissertation, we study the quadratic programming problem with discrete variables (DQP). DQP is important in theory and practice, but the combination of the quadratic feature of the objective function and the discrete nature of the feasible domain makes it hard to solve. In this th...

This paper deals with the competitive location problems using fuzzy sets. The basic notions on fuzzy optimization and linear programming using fuzzy sets are briefly reviewed. The standard leader-follower location problem and its linear mathematical programming formulation are described. The works appeared in the literature concerning the use of fuzzy sets are analyzed. Keywords— Fuzzy Optimiza...

Detecting infeasibility in conic optimization and providing certificates for infeasibility pose a bigger challenge than in the linear case due to the lack of strong duality. In this paper we generalize the approximate Farkas lemma of Todd and Ye [12] from the linear to the general conic setting, and use it to propose stopping criteria for interior point algorithms using self-dual embedding. The...

We study the convex hull of the intersection of a disjunctive set defined by parallel hyperplanes and the feasible set of a mixed integer second order cone optimization (MISOCO) problem. We extend our prior work on disjunctive conic cuts (DCCs), which has thus far been restricted to the case in which the intersection of the hyperplanes and the feasible set is bounded. Using a similar technique,...

Space tensors appear in physics and mechanics, and they are real physical entities. Mathematically, they are tensors in the three-dimensional Euclidean space. In the research of diffusion magnetic resonance imaging, convex optimization problems are formed where higher order positive semi-definite space tensors are involved. In this short paper, we investigate these problems from the viewpoint o...

In this paper we formulate the fuzzy bilevel programming problem and describe one possible approach for formulating a crisp optimization problem being attached to it. Due to the nature of fuzzy bilevel programming this is a crisp bilevel programming problem. We compare our approach with one using multicriterial optimization and show, that both approaches are basically different. The use of mult...

in this paper, a location allocation (la) problem in construction and demolition (c&d;) waste management (wm) is studied. a bi-level model for this problem under a fuzzy random environment is presented where the upper level is the governments who sets up the processing centers, and the lower level are the administrators of different construction projects who control c&d; waste and the after tre...

We present a strong duality theory for optimization problems over symmetric cones without assuming any constraint qualification. We show important complexity implications of the result to semidefinite and second order conic optimization. The result is an application of Borwein and Wolkowicz’s facial reduction procedure to express the minimal cone. We use Pataki’s simplified analysis and provide...