A stochastic gradient method for trilevel optimization

With the success that the field of bilevel optimization has seen in recent years, similar methodologies have started being applied to solving more difficult applications that arise in trilevel optimization. At the helm of these applications are new machine learning formulations that have been proposed in the trilevel context and, as a result, efficient and … Read more

An inexact alternating projection method with application to matrix completion

We develop and analyze an inexact regularized alternating projection method for nonconvex feasibility problems. Such a method employs inexact projections on one of the two sets, according to a set of well-defined conditions. We prove the global convergence of the algorithm, provided that a certain merit function satisfies the Kurdyka-Lojasiewicz property on its domain. The … Read more

Steepest descent method using novel adaptive stepsizes for unconstrained nonlinear multiobjective programming

We propose new adaptive strategies to compute stepsizes for the steepest descent method to solve unconstrained nonlinear multiobjective optimization problems without employing any linesearch procedure. The resulting algorithms can be applied to a wide class of nonconvex unconstrained multi-criteria optimization problems satisfying a global Lipschitz continuity condition imposed on the gradients of all objectives. In … Read more

a surplus-maximizing two-sided multi-period non-convex iso auction market

Since the inception of ISOs, Locational Marginal Prices (LMPs) alone were not market clearing or incentive compatible because an auction winner who offered its avoidable costs could lose money at the LMPs. ISOs used make-whole payments to ensure that market participants did not lose money. Make-whole payments were not public, creating transparency issues. Over time, … Read more

Quadratic Convex Reformulations for MultiObjective Binary Quadratic Programming

Multiobjective binary quadratic programming refers to optimization problems involving multiple quadratic – potentially non-convex – objective functions and a feasible set that includes binary constraints on the variables. In this paper, we extend the well-established Quadratic Convex Reformulation technique, originally developed for single-objective binary quadratic programs, to the multiobjective setting. We propose a branch-and-bound algorithm … Read more

On image space transformations in multiobjective optimization

This paper considers monotone transformations of the objective space of multiobjective optimization problems which leave the set of efficient points invariant. Under mild assumptions, for the standard ordering cone we show that such transformations must be component-wise transformations. The same class of transformations also leaves the sets of weakly and of Geoffrion properly efficient points … Read more

A Survey on the Applications of Stochastic Dual Dynamic Programming and its Variants

Stochastic Dual Dynamic Programming (SDDP) is widely recognized as the predominant methodology for solving large-scale multistage stochastic linear programming (MSLP) problems. This paper aims to contribute to the extant literature by conducting a comprehensive survey of the literature on SDDP within the realm of practical applications. We systematically identify and analyze the various domains where … Read more

Time Complexity and Optimality of Inventory and Production Policies for a Dynamic Lot Sizing Model with Remanufacturing and Separate Setup Costs

In this paper, we consider a dynamic lot sizing model with remanufacturing having m types of cores. The model also allows manufacturing. We consider separate setup costs for manufacturing and remanufacturing in our model. It is conjectured in [15], with reference to [18], that finding an optimal policy to the model when there is separate … Read more

The improvement function reformulation for graphs of minimal point mappings

Graphs of minimal point mappings of parametric optimization problems appear in the definition of feasible sets of bilevel optimization problems and of semi-infinite optimization problems, and the intersection of multiple such graphs defines (generalized) Nash equilibria. This paper shows how minimal point graphs of nonconvex parametric optimization problems can be written with the help of … Read more

An interactive optimization framework for incorporating a broader range of human feedback into stochastic multi-objective mixed integer linear programs

Interactive optimization leverages the strengths of optimization frameworks alongside the expertise of human users. Prior research in this area tends to either ask human users for the same type of information, or when varying information is requested, users must manually modify the optimization model directly. These limitations restrict the incorporation of wider human knowledge into … Read more