The purpose of this paper is to extend, as much as possible, the modern theory of condition numbers for conic convex optimization: z∗ := minx ctx s.t. Ax− b ∈ CY x ∈ CX , to the more general non-conic format: (GPd) z∗ := minx ctx s.t. Ax− b ∈ CY x ∈ P , where P is any closed convex set, not necessarily a cone, which we call the groundset. Although any convex problem can be transformed to conic ...

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...

although many methods exist for intensity modulated radiotherapy (imrt) fluence map optimization for crisp data, based on clinical practice, some of the involved parameters are fuzzy. in this paper, the best fluence maps for an imrt procedure were identifed as a solution of an optimization problem with a quadratic objective function, where the prescribed target dose vector was fuzzy. first, a d...

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...

A conic integer program is an integer programming problem with conic constraints. Many problems in finance, engineering, statistical learning, and probabilistic optimization are modeled using conic constraints. Here we study mixed-integer sets defined by second-order conic constraints. We introduce general-purpose cuts for conic mixed-integer programming based on polyhedral conic substructures ...

Conic optimization is the problem of optimizing a linear function over an intersection of an affine linear manifold with the Cartesian product of convex cones. However, many real world conic models involves an intersection rather than the product of two or more cones. It is easy to deal with an intersection of one or more cones but unfortunately it leads to an expansion in the optimization prob...

We reformulate the problem of modularity maximization over the set of partitions of a network as a conic optimization problem over the completely positive cone, converting it from a combinatorial optimization problem to a convex continuous one. A semidefinite relaxation of this conic program then allows to compute upper bounds on the maximum modularity of the network. Based on the solution of t...