Related papers: A new algorithm for constraint satisfaction proble…
We consider methods for aggregating preferences that are based on the resolution of discrete optimization problems. The preferences are represented by arbitrary binary relations (possibly weighted) or incomplete paired comparison matrices.…
We present a new feasible proximal gradient method for constrained optimization where both the objective and constraint functions are given by the summation of a smooth, possibly nonconvex function and a convex simple function. The…
Stochastic local search algorithms are frequently used to numerically solve hard combinatorial optimization or decision problems. We give numerical and approximate analytical descriptions of the dynamics of such algorithms applied to random…
A general class of nonconvex optimization problems is considered, where the penalty is the composition of a linear operator with a nonsmooth nonconvex mapping, which is concave on the positive real line. The necessary optimality condition…
This paper explores recent progress related to constraint maps. Building on the exposition in [14], our goal is to provide a clear and accessible account of some of the more intricate arguments behind the main results in this work. Along…
We present the viewpoint that optimization problems encountered in machine learning can often be interpreted as minimizing a convex functional over a function space, but with a non-convex constraint set introduced by model parameterization.…
The problem of optimizing a linear objective function,given a number of linear constraints has been a long standing problem ever since the times of Kantorovich, Dantzig and von Neuman. These developments have been followed by a different…
We propose a stochastic variance reduced optimization algorithm for solving sparse learning problems with cardinality constraints. Sufficient conditions are provided, under which the proposed algorithm enjoys strong linear convergence…
The promise constraint satisfaction problem (PCSP) is a recently introduced vast generalisation of the constraint satisfaction problem (CSP) that captures approximability of satisfiable instances. A PCSP instance comes with two forms of…
We propose an algorithm for optimizations in which the gradients contain stochastic noise. This arises, for example, in structural optimizations when computations of forces and stresses rely on methods involving Monte Carlo sampling, such…
In this paper we consider convex optimization problems with stochastic composite objective function subject to (possibly) infinite intersection of constraints. The objective function is expressed in terms of expectation operator over a sum…
We propose a framework to use Nesterov's accelerated method for constrained convex optimization problems. Our approach consists of first reformulating the original problem as an unconstrained optimization problem using a continuously…
Convex nonsmooth optimization problems, whose solutions live in very high dimensional spaces, have become ubiquitous. To solve them, the class of first-order algorithms known as proximal splitting algorithms is particularly adequate: they…
We describe a general parameterized scheme of program and constraint analyses allowing us to specify both the program specialization method known as Turchin's supercompilation and Hmelevskii's algorithm solving the quadratic word equations.…
To model combinatorial decision problems involving uncertainty and probability, we introduce stochastic constraint programming. Stochastic constraint programs contain both decision variables (which we can set) and stochastic variables…
In this paper, we propose some new semidefinite relaxations for a class of nonconvex complex quadratic programming problems, which widely appear in the areas of signal processing and power system. By deriving new valid constraints to the…
In this paper we consider non-smooth convex optimization problems with (possibly) infinite intersection of constraints. In contrast to the classical approach, where the constraints are usually represented as intersection of simple sets,…
Iterative linear solvers have gained recent popularity due to their computational efficiency and low memory footprint for large-scale linear systems. The relaxation method, or Motzkin's method, can be viewed as an iterative method that…
We study interactions between Skolem Arithmetic and certain classes of Constraint Satisfaction Problems (CSPs). We revisit results of Glass er et al. in the context of CSPs and settle the major open question from that paper, finding a…
We present a powerful general framework for designing data-dependent optimization algorithms, building upon and unifying recent techniques in adaptive regularization, optimistic gradient predictions, and problem-dependent randomization. We…