An Adaptive Patch Approximation Algorithm for Bicriteria Convex Mixed Integer problems

Pareto frontiers of bicriteria continuous convex problems can be efficiently computed and optimal theoretical performance bounds have been established. In the case of bicriteria mixed-integer problems, the approximation of the Pareto frontier becomes, however, significantly harder. In this paper, we propose a new algorithm for approximating the Pareto frontier of bicriteria mixed-integer programs with convex … Read more

On Refinement Strategies for Solving MINLPs by Piecewise Linear Relaxations: A Generalized Red Refinement

We investigate the generalized red refinement for n-dimensional simplices that dates back to Freudenthal in a mixed-integer nonlinear program (MINLP) context. We show that the red refinement meets sufficient convergence conditions for a known MINLP solution framework that is essentially based on solving piecewise linear relaxations. In addition, we prove that applying this refinement procedure … Read more

An Almost Exact Solution to the Min Completion Time Variance in a Single Machine

We consider a single machine scheduling problem to minimize the completion time variance of n jobs. This problem is known to be NP-hard and our contribution is to establish a novel bounding condition for a characterization of an optimal sequence. Specifically, we prove a necessary and sufficient condition (which can be verified in O(n\log n)) … Read more

Data-driven sample average approximation with covariate information

We study optimization for data-driven decision-making when we have observations of the uncertain parameters within the optimization model together with concurrent observations of covariates. Given a new covariate observation, the goal is to choose a decision that minimizes the expected cost conditioned on this observation. We investigate three data-driven frameworks that integrate a machine learning … Read more

Power to Air-transportation via Hydrogen

This paper proposes a framework to analyze the concept of power to hydrogen (P2H) for fueling the next generation of aircraft. The impact of introducing new P2H loads is investigated from different aspects namely, cost, carbon emission, and wind curtailment. The newly introduced electric load is calculated based on the idea of replacing the busiest … Read more

On the best achievable quality of limit points of augmented Lagrangian schemes

The optimization literature is vast in papers dealing with improvements on the global convergence of augmented Lagrangian schemes. Usually, the results are based on weak constraint qualifications, or, more recently, on sequential optimality conditions obtained via penalization techniques. In this paper we propose a somewhat different approach, in the sense that the algorithm itself is … Read more

LQR Design under Stability Constraints

The solution of classic discrete-time, finite-horizon linear quadratic regulator (LQR) problem is well known in literature. By casting the solution to be a static state-feedback, we propose a new method that trades off low LQR objective value with closed-loop stability. Citation To appear on the special issue on the 21st IFAC World Congress 2020, IFAC … Read more

Accelerated Inexact Composite Gradient Methods for Nonconvex Spectral Optimization Problems

This paper presents two inexact composite gradient methods, one inner accelerated and another doubly accelerated, for solving a class of nonconvex spectral composite optimization problems. More specifically, the objective function for these problems is of the form f_1 + f_2 + h where f_1 and f_2 are differentiable nonconvex matrix functions with Lipschitz continuous gradients, … Read more

Zeroth-Order Algorithms for Nonconvex Minimax Problems with Improved Complexities

In this paper, we study zeroth-order algorithms for minimax optimization problems that are nonconvex in one variable and strongly-concave in the other variable. Such minimax optimization problems have attracted significant attention lately due to their applications in modern machine learning tasks. We first design and analyze the Zeroth-Order Gradient Descent Ascent (ZO-GDA) algorithm, and provide … Read more

Accelerated Dual-Averaging Primal-Dual Method for Composite Convex Minimization

Dual averaging-type methods are widely used in industrial machine learning applications due to their ability to promoting solution structure (e.g., sparsity) efficiently. In this paper, we propose a novel accelerated dual-averaging primal-dual algorithm for minimizing a composite convex function. We also derive a stochastic version of the proposed method which solves empirical risk minimization, and … Read more