The paper is devoted to the study of general nonsmooth problems of cone-constrained optimization (or conic programming) important for various aspects of optimization theory and applications. Based on advanced constructions and techniques of variational analysis and generalized differentiation, we derive new necessary optimality conditions (in both " exact " and " fuzzy " forms) for nonsmooth co...

We study split cuts and extended formulations for Mixed Integer Conic Quadratic Programming (MICQP) and their relation to Conic Mixed Integer Rounding (CMIR) cuts. We show that CMIR is a linear split cut for the polyhedral portion of an extended formulation of a quadratic set and it can be weaker than the nonlinear split cut of the same quadratic set. However, we also show that families of CMIR...

We show in this paper that Eq. (1) can be solved exactly in linear time. The procedure aims at solving a dual formulation of Eq. (1) involving the dual norm of ‖.‖ denoted by ‖.‖∗ and defined as ‖κ‖∗ = max‖z‖≤1 zκ for any vector κ in R. We first derive a dual problem based on conic duality [Boyd and Vandenberghe, 2004]. The rationale for using conic duality is to come up with a dual problem wit...

Given a switched system formed by a pair of (not asymptotically stable) linear vector fields of R, we define a special class of hybrid feedback laws (called recurrent switching rules) whose structure depends on some conic regions with nonempty interior. We prove that if the system is asymptotically controllable and radially controllable, then it is robustly stabilized by any recurrent switching...

An interesting recent trend in optimization is the application of semidefinite programming techniques to new classes of optimization problems. In particular, this trend has been successful in showing that under suitable circumstances, polynomial optimization problems can be approximated via a sequence of semidefinite programs. Similar ideas apply to conic optimization over the cone of copositiv...

Catadioptric systems consist of the combination of lenses and mirrors [1]. From them, central panoramic systems stand out because they provide a unique effective viewpoint, leading to the well-known unifying theory for central catadioptric systems [4], [2]. This work considers catadioptric systems consisting of a conic mirror and a projective camera. Although a system with conic mirror does not...

This paper studies the constrained multi-location assortment optimization problem under joint delivery by drone and human courier. To maximize revenue of retailer, product last-mile methods are configured simultaneously. handle with assortment, a mixed multinomial logit model is established to depict customer purchase behavior. We also take into account load capacity drones distance limit couri...

We introduce several modifications of conic fitting in Geometric algebra for conics by incorporating additional conditions into the optimisation problem. Each these extra ensure geometric properties a fitted conic, particular, centre point position at origin coordinate system, axial alignment with axes, or, eventually, combination both. All derived algorithms are accompanied discussion underlyi...

Balas introduced intersection cuts for mixed integer linear sets. Intersection cuts are given by closed form formulas and form an important class of cuts for solving mixed integer linear programs. In this paper we introduce an extension of intersection cuts to mixed integer conic quadratic sets. We identify the formula for the conic quadratic intersection cut by formulating a system of polynomi...

In multiobjective optimization methods, multiple conflicting objectives are typically converted into a single objective optimization problem with the help of scalarizing functions. The conic scalarizing function is a general characterization of Benson proper efficient solutions of non-convex multiobjective problems in terms of saddle points of scalar Lagrangian functions. This approach preserve...