\(\) We introduce a notion of self-concordant smoothing for minimizing the sum of two convex functions, one of which is smooth and the other may be nonsmooth. The key highlight of our approach is in a natural property of the resulting problem’s structure which provides us with a variable-metric selection method and a step-length selection … Read more
We propose the use of a conjecturing machine that suggests feature relationships in the form of bounds involving nonlinear terms for numerical features and boolean expressions for categorical features. The proposed Conjecturing framework recovers known nonlinear and boolean relationships among features from data. In both settings, true underlying relationships are revealed. We then compare the … Read more
This paper is devoted to study the convergence rates of a second-order dynamical system and its corresponding discretization associated with a continuously differentiable bilinearly coupled convex-concave saddle point problem. First, we consider the second-order dynamical system with asymptotically vanishing damping term and show the existence and uniqueness of the trajectories as global twice continuously differentiable … Read more
In this paper, we propose an innovative variable fixing strategy called deep Lagrangian underestimate fixing (DeLuxing). It is a highly effective approach for removing unnecessary variables in column-generation (CG)-based exact methods used to solve challenging discrete optimization problems commonly encountered in various industries, including vehicle routing problems (VRPs). DeLuxing employs a novel linear programming (LP) … Read more
Article Download View The pseudo-Boolean polytope and polynomial-size extended formulations for binary polynomial optimization
\(\) We develop a new method called \emph{affine FR} for recovering Slater’s condition for semidefinite programming (SDP) relaxations of combinatorial optimization (CO) problems. Affine FR is a user-friendly method, as it is fully automatic and only requires a description of the problem. We provide a rigorous analysis of differences between affine FR and the existing … Read more
\(\) Positive spanning sets span a given vector space by nonnegative linear combinations of their elements. These have attracted significant attention in recent years, owing to their extensive use in derivative-free optimization. In this setting, the quality of a positive spanning set is assessed through its cosine measure, a geometric quantity that expresses how well … Read more
One of the chief attractions of stochastic mixed-integer second-order cone programming is its diverse applications, especially in engineering (Alzalg and Alioui, {\em IEEE Access}, 10:3522-3547, 2022). The linear and nonlinear versions of this class of optimization problems are still unsolved yet. In this paper, we develop a hybrid optimization algorithm coupling branch-and-bound and primal-dual interior-point … Read more
\(\) We consider linear combinatorial optimization problems under uncertain disruptions that increase the cost coefficients of the objective function. A decision-maker, or planner, can invest resources to probe the components (i.e., the coefficients) in order to learn their disruption status. In the proposed probing optimization problem, the planner, knowing just the disruptions’ probabilities, selects which … Read more
The convex-concave minimax problem, known as the saddle-point problem, has been extensively studied from various aspects including the algorithm design, convergence condition and complexity. In this paper, we propose a generalized asymmetric forward-backward-adjoint (G-AFBA) algorithm to solve such a problem by utilizing both the proximal techniques and the interactive information of primal-dual updates. Except enjoying … Read more