Convergence Analysis of Processes with Valiant Projection Operators in Hilbert Space

Convex feasibility problems require to find a point in the intersection of a finite family of convex sets. We propose to solve such problems by performing set-enlargements and applying a new kind of projection operators called valiant projectors. A valiant projector onto a convex set implements a special relaxation strategy, proposed by Goffin in 1971, … Read more

Modeling Time-dependent Randomness in Stochastic Dual Dynamic Programming

We consider the multistage stochastic programming problem where uncertainty enters the right-hand sides of the problem. Stochastic Dual Dynamic Programming (SDDP) is a popular method to solve such problems under the assumption that the random data process is stagewise independent. There exist two approaches to incorporate dependence into SDDP. One approach is to model the … Read more

Perturbation analysis of a class of conic programming problems under Jacobian uniqueness conditions

We consider the stability of a class of parameterized conic programming problems which are more general than the C2-smooth parameterization. We show that when the Karush-Kuhn-Tucker (KKT) condition, the constraint nondegeneracy condition, the strict complementary condition and the second order sucient condition (named as Jacobian uniqueness conditions here) are satis ed at a feasible point of … Read more

Robust Combinatorial Optimization under Convex and Discrete Cost Uncertainty

In this survey, we discuss the state-of-the-art of robust combinatorial optimization under uncertain cost functions. We summarize complexity results presented in the literature for various underlying problems, with the aim of pointing out the connections between the different results and approaches, and with a special emphasis on the role of the chosen uncertainty sets. Moreover, … Read more

Complementarity-Based Nonlinear Programming Techniques for Optimal Mixing in Gas Networks

We consider nonlinear and nonsmooth mixing aspects in gas transport optimization problems. As mixed-integer reformulations of pooling-type mixing models already render small-size instances computationally intractable, we investigate the applicability of smooth nonlinear programming techniques for equivalent complementarity-based reformulations. Based on recent results for remodeling piecewise affine constraints using an inverse parametric quadratic programming approach, we … Read more

Perturbation analysis of nonlinear semidefinite programming under Jacobian uniqueness conditions

We consider the stability of a class of parameterized nonlinear semidefinite programming problems whose objective function and constraint mapping all have second partial derivatives only with respect to the decision variable which are jointly continuous. We show that when the Karush-Kuhn-Tucker (KKT) condition, the constraint nondegeneracy condition, the strict complementary condition and the second order … Read more

Parsimonious formulations for low-diameter clusters

In the analysis of networks, one often searches for tightly knit clusters. One property of a “good” cluster is a small diameter (say, bounded by $k$), which leads to the concept of a $k$-club. In this paper, we propose new path-like and cut-like integer programming formulations for detecting these low-diameter subgraphs. They simplify, generalize, and/or … Read more

A General Regularized Continuous Formulation for the Maximum Clique Problem

In this paper, we develop a general regularization-based continuous optimization framework for the maximum clique problem. In particular, we consider a broad class of regularization terms that can be included in the classic Motzkin-Strauss formulation and we develop conditions that guarantee the equivalence between the continuous regularized problem and the original one in both a … Read more

FPBH.jl: A Feasibility Pump Based Heuristic for Multi-objective Mixed Integer Linear Programming in Julia

Feasibility pump is one of the successful heuristic solution approaches developed almost a decade ago for computing high-quality feasible solutions of single-objective integer linear programs, and it is implemented in exact commercial solvers such as CPLEX and Gurobi. In this study, we present the first Feasibility Pump Based Heuristic (FPBH) approach for approximately generating nondominated … Read more

Comparative Analysis of Capacitated Arc Routing Formulations for Branch-Cut-and-Price Algorithms

The current best exact algorithms for the Capacitated Arc Routing Problem are based on the combination of cut and column generation. This work presents a deep theoretical investigation of the formulations behind those algorithms, classifying them and pointing similarities and differences, advantages and disadvantages. In particular, we discuss which families of cuts and branching strategies … Read more