Globally Convergent Derivative-Free Methods in Nonconvex Optimization with and without Noise

This paper addresses the study of nonconvex derivative-free optimization problems, where only information of either smooth objective functions or their noisy approximations is available. General derivative-free methods are proposed for minimizing differentiable (not necessarily convex) functions with globally Lipschitz continuous gradients, where the accuracy of approximate gradients is interacting with stepsizes and exact gradient values. … Read more

BattOpt: Optimal Facility Planning for Electric Vehicle Battery Recycling

The electric vehicle (EV) battery supply chain will face challenges in sourcing scarce, expensive minerals required for manufacturing and in disposing of hazardous retired batteries. Integrating recycling technology into the supply chain has the potential to alleviate these issues; however, players in the battery market must design investment plans for recycling facilities. In this paper, … Read more

Incorporating Service Reliability in Multi-depot Vehicle Scheduling: A Chance-Constrained Approach

The multi-depot vehicle scheduling problem (MDVSP) is a critical planning challenge for transit agencies. We introduce a novel approach to MDVSP by incorporating service reliability through chance-constrained programming (CCP), targeting the pivotal issue of travel time uncertainty and its impact on transit service quality. Our model guarantees service reliability measured by on-time performance (OTP), a … Read more

Benders decomposition with scaled cuts for multistage stochastic mixed-integer programs

We consider Benders decomposition algorithms for multistage stochastic mixed-integer programs (SMIPs) with general mixed-integer decision variables at every node in the scenario tree. We derive a hierarchy of convex polyhedral lower bounds for the value functions and expected cost to-go functions in multistage SMIPs using affine parametric cutting planes in extended spaces for the feasible … Read more

MUSE-BB: A Decomposition Algorithm for Nonconvex Two-Stage Problems using Strong Multisection Branching

\(\) We present MUSE-BB, a branch-and-bound (B&B) based decomposition algorithm for the deterministic global solution of nonconvex two-stage stochastic programming problems. In contrast to three recent decomposition algorithms, which solve this type of problem in a projected form by nesting an inner B&B in an outer B&B on the first-stage variables, we branch on all … Read more

A four-operator splitting algorithm for nonconvex and nonsmooth optimization

\(\) In this work, we address a class of nonconvex nonsmooth optimization problems where the objective function is the sum of two smooth functions (one of which is proximable) and two nonsmooth functions (one proper, closed and proximable, and the other continuous and weakly concave). We introduce a new splitting algorithm that extends the Davis-Yin … Read more

A Subgradient Projection Method with Outer Approximation for Solving Semidefinite Programming Problems

We explore the combination of subgradient projection with outer approximation to solve semidefinite programming problems. We compare several ways to construct outer approximations using the problem structure. The resulting approach enjoys the strengths of both subgradient projection and outer approximation methods. Preliminary computational results on the semidefinite programming relaxations of graph partitioning and max-cut show … Read more

Projection onto hyperbolicity cones and beyond: a dual Frank-Wolfe approach

We discuss the problem of projecting a point onto an arbitrary hyperbolicity cone from both theoretical and numerical perspectives. While hyperbolicity cones are furnished with a generalization of the notion of eigenvalues, obtaining closed form expressions for the projection operator as in the case of semidefinite matrices is an elusive endeavour. To address that we … Read more

Complexity of Adagrad and other first-order methods for nonconvex optimization problems with bounds and convex constraints

A parametric class of trust-region algorithms for constrained nonconvex optimization is analyzed, where the objective function is never computed. By defining appropriate first-order stationarity criteria, we are able to extend the Adagrad method to the newly considered problem and retrieve the standard complexity rate of the projected gradient method that uses both the gradient and … Read more