On deterministic reformulations of distributionally robust joint chance constrained optimization problems

Categories Convex Optimization, Robust Optimization, Stochastic Programming Tags , , ,

A joint chance constrained optimization problem involves multiple uncertain constraints, i.e., constraints with stochastic parameters, that are jointly required to be satisfied with probability exceeding a prespecified threshold. In a distributionally robust joint chance constrained optimization problem (DRCCP), the joint chance constraint is required to hold for all probability distributions of the stochastic parameters from … Read more

Optimization with stochastic preferences based on a general class of scalarization functions

Categories Multi-Criteria Optimization, Stochastic Programming

It is of crucial importance to develop risk-averse models for multicriteria decision making under uncertainty. A major stream of the related literature studies optimization problems that feature multivariate stochastic benchmarking constraints. These problems typically involve a univariate stochastic preference relation, often based on stochastic dominance or a coherent risk measure such as conditional value-at-risk (CVaR), … Read more

On the convergence of a regularized Jacobi algorithm for convex optimization

Categories Nonsmooth Optimization Tags , , ,

In this paper we consider the regularized version of the Jacobi algorithm, a block coordinate descent method for convex optimization with differentiable objective function and block-separable constraints that has been recently proposed in the literature. Under certain regularity assumptions on the objective function, this algorithm has been shown to satisfy the so-called sufficient decrease condition, … Read more

Decomposition and Optimization in Constructing Forward Capacity Market Demand Curves

Categories Applications - Science and Engineering, Finance and Economics Tags , , , , , , ,

This paper presents an economic framework for designing demand curves in Forward Capacity Market (FCM). Capacity demand curves have been recognized as a way to reduce the price volatility inherited from fixed capacity requirements. However, due to the lack of direct demand bidding in FCM, obtaining demand curves that appropriately reflect load’s willingness to pay … Read more

Positive-Indefinite Proximal Augmented Lagrangian Method and its Application to Full Jacobian Splitting for Multi-block Separable Convex Minimization Problems

Categories Convex Optimization Tags , , , , , ,

The augmented Lagrangian method (ALM) is fundamental for solving convex programming problems with linear constraints. The proximal version of ALM, which regularizes ALM’s subproblem over the primal variable at each iteration by an additional positive-definite quadratic proximal term, has been well studied in the literature. In this paper, we show that it is not necessary … Read more

Accelerated gradient sliding for structured convex optimization

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

Our main goal in this paper is to show that one can skip gradient computations for gradient descent type methods applied to certain structured convex programming (CP) problems. To this end, we first present an accelerated gradient sliding (AGS) method for minimizing the summation of two smooth convex functions with different Lipschitz constants. We show … Read more

Quadratic Two-Stage Stochastic Optimization with Coherent Measures of Risk

Categories Linear, Cone and Semidefinite Programming, Robust Optimization, Stochastic Programming

A new scheme to cope with two-stage stochastic optimization problems uses a risk measure as the objective function of the recourse action, where the risk measure is defined as the worst-case expected values over a set of constrained distributions. This paper develops an approach to deal with the case where both the first and second … Read more

Regularized nonlinear acceleration

Categories Convex Optimization, Unconstrained Optimization Tags

We describe a convergence acceleration technique for generic optimization problems. Our scheme computes estimates of the optimum from a nonlinear average of the iterates produced by any optimization method. The weights in this average are computed via a simple linear system, whose solution can be updated online. This acceleration scheme runs in parallel to the … Read more

Ambiguous Risk Constraints with Moment and Unimodality Information

Categories Robust Optimization, Stochastic Programming Tags , , , , ,

Optimization problems face random constraint violations when uncertainty arises in constraint parameters. Effective ways of controlling such violations include risk constraints, e.g., chance constraints and conditional Value-at-Risk (CVaR) constraints. This paper studies these two types of risk constraints when the probability distribution of the uncertain parameters is ambiguous. In particular, we assume that the distributional … Read more

Pseudo basic steps: Bound improvement guarantees from Lagrangian decomposition in convex disjunctive programming

Categories (Mixed) Integer Nonlinear Programming Tags , , , ,

An elementary, but fundamental, operation in disjunctive programming is a basic step, which is the intersection of two disjunctions to form a new disjunction. Basic steps bring a disjunctive set in regular form closer to its disjunctive normal form and, in turn, produce relaxations that are at least as tight. An open question is: What … Read more