We present a convex conic relaxation for a problem of maximizing an indefinite quadratic form over a set of convex constraints on the squared variables. We show that for all these problems we get at least 12 37 -relative accuracy of the approximation. In the second part of the paper we derive the conic relaxation by another approach based on the second order optimality conditions. We show that ...

Infinite-dimensional linear conic formulations are described for nonlinear optimal control problems. The primal linear problem consists of finding occupation measures supported on optimal relaxed controlled trajectories, whereas the dual linear problem consists of finding the largest lower bound on the value function of the optimal control problem. Various approximation results relating the ori...

We address the inverse problem of Lagrangian identification based on trajectories in the context of nonlinear optimal control. We propose a general formulation of the inverse problem based on occupation measures and complementarity in linear programming. The use of occupation measures in this context offers several advantages from the theoretical, numerical and statistical points of view. We pr...

A novel linear feature selection algorithm is presented based on the global minimization of a data-dependent generalization error bound. Feature selection and scaling algorithms often lead to non-convex optimization problems, which in many previous approaches were addressed through gradient descent procedures that can only guarantee convergence to a local minimum. We propose an alternative appr...

The primal-dual Dikin-type affine scaling method was originally proposed for linear optimization and then extended to semidefinite optimization. Here, the method is generalized to symmetric conic optimization using the notion of Euclidean Jordan algebras. The method starts with an interior feasible but not necessarily centered primal-dual solution, and it features both centering and reducing th...

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 study how to solve sum of squares (SOS) and Lasserre’s relaxations for large scale polynomial optimization. When interior-point type methods are used, typically only small or moderately large problems could be solved. This paper proposes the regularization type methods which would solve significantly larger problems. We first describe these methods for general conic semidefinite optimization...

In this paper, we consider a stochastic Time-Cost Tradeoff Problem (TCTP) in PERT networks for project management, in which all activities are subjected to a linear cost function and assumed to be exponentially distributed. The aim of this problem is to maximize the project completion probability with a pre-known deadline to a predefined probability such that the required additional cost is min...

Slater’s condition – existence of a “strictly feasible solution” – is a common assumption in conic optimization. Without strict feasibility, first-order optimality conditions may be meaningless, the dual problem may yield little information about the primal, and small changes in the data may render the problem infeasible. Hence, failure of strict feasibility can negatively impact off-the-shelf ...

In this paper, we implement Zhang’s method [22], which transforms a general convex optimization problem with smooth convex constraints into a convex conic optimization problem and then apply the techniques of self-dual embedding and central path following for solving the resulting conic optimization model. A crucial advantage of the approach is that no initial solution is required, and the meth...