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We employ chordal decomposition to reformulate a large and sparse semidefinite program (SDP), either in primal or dual standard form, into an equivalent SDP with smaller positive semidefinite (PSD) constraints. In contrast to previous…

We study a class of bilevel integer programs with second-order cone constraints at the upper level and a convex quadratic objective and linear constraints at the lower level. We develop disjunctive cuts to separate bilevel infeasible points…

Smooth minimax optimization problems play a central role in a wide range of applications, including machine learning, game theory, and operations research. However, existing algorithmic frameworks vary significantly depending on the problem…

To deal with various datasets over different complexity, this paper presents an self-adaptive learning model that combines the proposed Dynamic Connected Neural Decision Networks (DNDN) and a new pruning method--Dynamic Soft Pruning (DSP).…

Stochastic Gradient Descent-Ascent (SGDA) is one of the most prominent algorithms for solving min-max optimization and variational inequalities problems (VIP) appearing in various machine learning tasks. The success of the method led to…

In this paper, we study a fixed-confidence, fixed-tolerance formulation of a class of stochastic bi-level optimization problems, where the upper-level problem selects from a finite set of systems based on a performance metric, and the…

In this paper, we introduce a new class of decision rules, referred to as Constant Depth Decision Rules (CDDRs), for multistage optimization under linear constraints with uncertainty-affected right-hand sides. We consider two uncertainty…

We consider the large sum of DC (Difference of Convex) functions minimization problem which appear in several different areas, especially in stochastic optimization and machine learning. Two DCA (DC Algorithm) based algorithms are proposed:…

The optimization of chemical processes is challenging due to the nonlinearities arising from process physics and discrete design decisions. In particular, optimal synthesis and design of chemical processes can be posed as a Generalized…

We consider the problem of controlling a Markov decision process (MDP) with a large state space, so as to minimize average cost. Since it is intractable to compete with the optimal policy for large scale problems, we pursue the more modest…

Multi-stage stochastic linear programs (MSLPs) are notoriously hard to solve in general. Linear decision rules (LDRs) yield an approximation of an MSLP by restricting the decisions at each stage to be an affine function of the observed…

Network design problems involve constructing edges in a transportation or supply chain network to minimize construction and daily operational costs. We study a stochastic version where operational costs are uncertain due to fluctuating…

Stochastic gradient descent type methods are ubiquitous in machine learning, but they are only applicable to the optimization of differentiable functions. Proximal algorithms are more general and applicable to nonsmooth functions. We…

Logic-Based Benders Decomposition (LBBD) and its Branch-and-Cut variant, namely Branch-and-Check, enjoy an extensive applicability on a broad variety of problems, including scheduling. Although LBBD offers problem-specific cuts to impose…

A stochastic program typically involves several parameters, including deterministic first-stage parameters and stochastic second-stage elements that serve as input data. These programs are re-solved whenever any input parameter changes.…

In networks, there are often more than one source of capacity. The capacities can be permanently or temporarily owned by the decision maker. Depending on the nature of sources, we identify the permanent capacity, spot market capacity and…

Bayesian modelling enables us to accommodate complex forms of data and make a comprehensive inference, but the effect of partial misspecification of the model is a concern. One approach in this setting is to modularize the model, and…

Truckload procurement plays a vital role in integrated container logistics, particularly under the uncertainties of container flow and market conditions. We formulate the operational volume allocation problem in drayage procurement as a…

Balancing between computational efficiency and sample efficiency is an important goal in reinforcement learning. Temporal difference (TD) learning algorithms stochastically update the value function, with a linear time complexity in the…

We consider stochastic convex optimization problems where the objective is an expectation over smooth functions. For this setting we suggest a novel gradient estimate that combines two recent mechanism that are related to notion of…