the mathematical aspect of cartographic mapping is a process which establishes a unique connection between points of the earth’s sphere and their images on a plane. it was proven in differential geometry that an isometric mapping of a sphere onto a plane with all corresponding distances on both surfaces remaining identical can never be achieved since the two surfaces do not possess the same gau...

We consider the pricing problem faced by a retailer endowed with a finite inventory of a product offered over a finite planning horizon in an environment where customers are price-sensitive. The parameters of the product demand curve are fixed but unknown to the seller who only has at his disposal a history of sales data. We propose an adaptive optimization approach to setting prices that captu...

In this paper we introduce a conic optimization formulation for inequality-constrained convex programming, and propose a self-dual embedding model for solving the resulting conic optimization problem. The primal and dual cones in this formulation are characterized by the original constraint functions and their corresponding conjugate functions respectively. Hence they are completely symmetric. ...

We study the convex hull of the intersection of a convex set E and a disjunctive set. This intersection is at the core of solution techniques for Mixed Integer Convex Optimization. We prove that if there exists a cone K (resp., a cylinder C) that has the same intersection with the boundary of the disjunction as E , then the convex hull is the intersection of E with K (resp., C). The existence o...

JuMP is an algebraic modeling language embedded in the Julia programming language. allows users to model optimization problems of a variety kinds, including linear programming, integer conic optimization, semidefinite and nonlinear handles low-level details communicating with solvers. After nearly 10 years development, 1.0 was released March, 2022. In this short communication, we highlight impr...

A conic integer program is an integer programming problem with conic constraints. Conic integer programming has important applications in finance, engineering, statistical learning, and probabilistic integer programming. Here we study mixed-integer sets defined by second-order conic constraints. We describe general-purpose conic mixed-integer rounding cuts based on polyhedral conic substructure...

This paper proposes a calibration method for catadioptric camera systems consisting of a surface of revolution mirror and a perspective camera, such as HyperOmni Vision. The proposed method is based on conventional camera calibration and mirror posture estimation. Many methods for camera calibration have been proposed. During the last decade, methods for catadioptric camera calibration have als...

We consider a distributionally robust optimization problem where the ambiguity set of probability distributions is characterized by a tractable conic representable support set and expectation constraints. Specifically, we propose and motivate a new class of infinitely constrained ambiguity sets in which the number of expectation constraints could potentially be infinite. We show how the infinit...