Chance constrained nonlinear optimization with skewed distributions and dependent rows

Categories Stochastic Programming Tags , , , ,

This paper discusses chance constrained optimization problems where the constraints are linear to the random variables but nonlinear to the decision variables. For the individual nonlinear chance constraint, we derive tractable reformulation under finite Gaussian mixture distributions and design tight approximation under the generalized hyperbolic distribution. For the joint nonlinear chance constraint, we study several … Read more

A Trust Region Method for the Optimization of Noisy Functions

Categories Nonlinear Optimization Tags , ,

Classical trust region methods were designed to solve problems in which function and gradient information are exact. This paper considers the case when there are bounded errors (or noise) in the above computations and proposes a simple modification of the trust region method to cope with these errors. The new algorithm only requires information about … Read more

Time-series aggregation for the optimization of energy systems: goals, challenges, approaches, and opportunities

Categories Data-Mining, Energy, Facility Planning and Design Tags , , , , ,

The rising significance of renewable energy increases the importance of representing time-varying input data in energy system optimization studies. Time-series aggregation, which reduces temporal model complexity, has emerged in recent years to address this challenge. We provide a comprehensive review of time-series aggregation for the optimization of energy systems. We show where time series affect … Read more

On the convex hull of convex quadratic optimization problems with indicators

Categories (Mixed) Integer Nonlinear Programming Tags , ,

We consider the convex quadratic optimization problem with indicator variables and arbitrary constraints on the indicators. We show that a convex hull description of the associated mixed-integer set in an extended space with a quadratic number of additional variables consists of a single positive semidefinite constraint (explicitly stated) and linear constraints. In particular, convexification of … Read more

An Algorithm for Stochastic Convex-Concave Fractional Programs with Applications to Production Efficiency and Equitable Resource Allocation

Categories Global Optimization, Global Optimization Applications, Stochastic Approaches Tags , , , ,

We propose an algorithm to solve convex and concave fractional programs and their stochastic counterparts in a common framework. Our approach is based on a novel reformulation that involves differences of square terms in the constraints, and subsequent employment of piecewise-linear approximations of the concave terms. Using the branch-and-bound (B&B) framework, our algorithm adaptively refines … Read more

Graph topology invariant gradient and sampling complexity for decentralized and stochastic optimization

Categories Convex and Nonsmooth Optimization, Nonlinear Optimization, Stochastic Programming Tags , , ,

One fundamental problem in decentralized multi-agent optimization is the trade-off between gradient/sampling complexity and communication complexity. We propose new algorithms whose gradient and sampling complexities are graph topology invariant, while their communication complexities remain optimal. For convex smooth deterministic problems, we propose a primal dual sliding (PDS) algorithm that computes an $\epsilon$-solution with $O((\tilde{L}/\epsilon)^{1/2})$ gradient … Read more

Optimal Robust Policy for Feature-Based Newsvendor

Categories Infinite Dimensional Optimization, Robust Optimization, Supply Chain Management Tags , , ,

We study policy optimization for the feature-based newsvendor, which seeks an end-to-end policy that renders an explicit mapping from features to ordering decisions. Unlike existing works that restrict the policies to some parametric class which may suffer from sub-optimality (such as affine class) or lack of interpretability (such as neural networks), we aim to optimize … Read more

Affine invariant convergence rates of the conditional gradient method

Categories Convex Optimization Tags , , ,

We show that the conditional gradient method for the convex composite problem \[\min_x\{f(x) + \Psi(x)\}\] generates primal and dual iterates with a duality gap converging to zero provided a suitable growth property holds and the algorithm makes a judicious choice of stepsizes. The rate of convergence of the duality gap to zero ranges from sublinear … Read more

Worst-Case Complexity of an SQP Method for Nonlinear Equality Constrained Stochastic Optimization

Categories Constrained Nonlinear Optimization, Stochastic Programming Tags , , ,

A worst-case complexity bound is proved for a sequential quadratic optimization (commonly known as SQP) algorithm that has been designed for solving optimization problems involving a stochastic objective function and deterministic nonlinear equality constraints. Barring additional terms that arise due to the adaptivity of the monotonically nonincreasing merit parameter sequence, the proved complexity bound is … Read more

Metaheuristic, Models and Software for the Heterogeneous Fleet Pickup and Delivery Problem with Split Loads

Categories Meta Heuristics, Optimization Software and Modeling Systems, Transportation Tags , , , ,

This paper addresses a rich variant of the vehicle routing problem (VRP) that involves pickup and delivery activities, customer time windows, heterogeneous fleet, multiple products and the possibility of splitting a customer demand among several routes. This variant generalizes traditional VRP variants by incorporating features that are commonly found in practice. We present two mixed-integer … Read more