In this paper, we propose a calibration method for catadioptric camera sy stems consisting of a rotation symmetry mirror, like H yperO mni V ision, and an affi ne camera. T he proposed method is based on conventional camera calibration and mirror postu re estimation. M any methods for camera calibration have previou sly been proposed. In the last decade, methods for catadioptric camera calibrat...

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...

We develop a modular and tractable framework for solving a distributionally adaptive optimization problem, where we minimize the worst-case expected cost over an ambiguity set of probability distributions. The adaptive optimization framework caters for dynamic decision making, where decisions can adapt to the uncertain outcomes as they unfold in stages. We propose a second-order conic (SOC) rep...

We develop a modular and tractable framework for solving an adaptive distributionally robust linear optimization problem, where we minimize the worst-case expected cost over an ambiguity set of probability distributions. The adaptive distrbutaionally robust optimization framework caters for dynamic decision making, where decisions can adapt to the uncertain outcomes as they unfold in stages. Fo...

This paper develops a linear programming based branch-and-bound algorithm for mixed integer conic quadratic programs. The algorithm is based on a higher dimensional or lifted polyhedral relaxation of conic quadratic constraints introduced by Ben-Tal and Nemirovski. The algorithm is different from other linear programming based branch-and-bound algorithms for mixed integer nonlinear programs in ...

Duality theory is important in finding solutions to optimization problems. For example, linear programming problems, the primal and dual problem pairs are closely related, i.e., if optimal solution of one known, then for other can be obtained easily. In order an solved through dual, first step formulate its analyze characteristics. this paper, we construct model uncertain multi-objective as wel...

We present a novel algorithm, Random Conic Pursuit, that solves semidefinite programs (SDPs) via repeated optimization over randomly selected two-dimensional subcones of the PSD cone. This scheme is simple, easily implemented, applicable to very general SDPs, scalable, and theoretically interesting. Its advantages are realized at the expense of an ability to readily compute highly exact solutio...

We show that the robust counterpart of a convex quadratic constraint with ellipsoidal implementation error is equivalent to a system of conic quadratic constraints. To prove this result we first derive a sharper result for the S-lemma in case the two matrices involved can be simultaneously diagonalized. This extension of the S-lemma may also be useful for other purposes. We extend the result to...

This paper considers generation self-scheduling in electricity markets under uncertain price. Based on the robust optimization denoted as RO methodology, a new self-scheduling model, which has a complicated max-min optimization structure, is set up. By using optimal dual theory, the proposed model is reformulated to an ordinary quadratic and quadratic cone programming problems in the cases of b...