In this paper we study the Consistent Traveling Salesman Problem with positional consistency constraints (CTSP), where we seek to generate a set of routes with minimum cost, in which all the clients that are visited in several routes require total positional consistency, that is, they need to appear in the same relative position in all … Read more
Motivated by recent progress on online linear programming (OLP), we study the online decision making problem (ODMP) as a natural generalization of OLP. In ODMP, there exists a single decision maker who makes a series of decisions spread out over a total of \(T\) time stages. At each time stage, the decision maker makes a … Read more
DP is a complexity class that is the class of all languages that are the intersection of a language in NP and a language in co-NP, as coined by Papadimitriou and Yannakakis. In this paper, we will establish that, recognizing a facet for the knapsack polytope is DP-complete, as conjectured by Hartvigsen and Zemel in … Read more
In this paper, the symbol detection mean squared error (MSE) constrained hybrid analog and digital beamforming is proposed in millimeter wave (mmWave) system, and the reconfigurable intelligent surface (RIS) is proposed to assist the mmWave system. The inner majorization-minimization (iMM) method is proposed to obtain analog transmitter, RIS and analog receivers, and the alternating direction … Read more
We consider a class of Riemannian optimization problems where the objective is the sum of a smooth function and a nonsmooth function, considered in the ambient space. This class of problems finds important applications in machine learning and statistics such as the sparse principal component analysis, sparse spectral clustering, and orthogonal dictionary learning. We propose … Read more
We consider the projected gradient algorithm for the nonconvex best subset selection problem that minimizes a given empirical loss function under an \(\ell_0\)-norm constraint. Through decomposing the feasible set of the given sparsity constraint as a finite union of linear subspaces, we present two acceleration schemes with global convergence guarantees, one by same-space extrapolation and … Read more
Adjustable Robust Optimization (ARO) is a paradigm for facing uncertainty in a decision problem, in case some recourse actions are allowed after the actual value of all input parameters is revealed. While several approaches have been introduced for the linear case, little is known regarding exact methods for the convex case. In this work, we … Read more
A convex cone is homogeneous if its automorphism group acts transitively on the interior of the cone, i.e., for every pair of points in the interior of the cone, there exists a cone automorphism that maps one point to the other. Cones that are homogeneous and self-dual are called symmetric. The symmetric cones include the … Read more
We consider the proximal-gradient method for minimizing an objective function that is the sum of a smooth function and a non-smooth convex function. A feature that distinguishes our work from most in the literature is that we assume that the associated proximal operator does not admit a closed-form solution. To address this challenge, we study … Read more
Two-stage stochastic programs with binary recourse are challenging to solve and efficient solution methods for such problems have been limited. In this work, we generalize an existing binary decision diagram-based (BDD-based) approach of Lozano and Smith (Math. Program., 2018) to solve a special class of two-stage stochastic programs with binary recourse. In this setting, the … Read more