Related papers: Piecewise Linear Valued CSPs Solvable by Linear Pr…
A valued constraint satisfaction problem (VCSP) instance $(V,\Pi,w)$ is a set of variables $V$ with a set of constraints $\Pi$ weighted by $w$. Given a VCSP instance, we are interested in a re-weighted sub-instance $(V,\Pi'\subset \Pi,w')$…
The multi-objective optimization is to optimize several objective functions over a common feasible set. Since the objectives usually do not share a common optimizer, people often consider (weakly) Pareto points. This paper studies…
Recent research in areas such as SAT solving and Integer Linear Programming has shown that the performances of a single arbitrarily efficient solver can be significantly outperformed by a portfolio of possibly slower on-average solvers. We…
We investigate the use of linear programming tools for solving semidefinite programming relaxations of quadratically constrained quadratic problems. Classes of valid linear inequalities are presented, including sparse PSD cuts, and…
Polynomial optimization problems represent a wide class of optimization problems, with a large number of real-world applications. Current approaches for polynomial optimization, such as the sum of squares (SOS) method, rely on large-scale…
Designing complex engineered systems requires managing tightly coupled trade-offs between subsystem capabilities and resource requirements. Monotone co-design provides a compositional language for such problems, but its generality does not…
Recent advances in robot skill learning have unlocked the potential to construct task-agnostic skill libraries, facilitating the seamless sequencing of multiple simple manipulation primitives (aka. skills) to tackle significantly more…
Many fundamental problems in artificial intelligence, knowledge representation, and verification involve reasoning about sets and relations between sets and can be modeled as set constraint satisfaction problems (set CSPs). Such problems…
We study the complexity of the Distributed Constraint Satisfaction Problem (DCSP) on a synchronous, anonymous network from a theoretical standpoint. In this setting, variables and constraints are controlled by agents which communicate with…
Constraint Satisfaction Problems (CSPs) form a broad class of combinatorial problems, which can be formulated as homomorphism problems between relational structures. The CSP dichotomy theorem classifies all such problems over finite domains…
Signomial programs (SPs) are optimization problems specified in terms of signomials, which are weighted sums of exponentials composed with linear functionals of a decision variable. SPs are non-convex optimization problems in general, and…
A Datalog program solves a constraint satisfaction problem (CSP) if and only if it derives the goal predicate precisely on the unsatisfiable instances of the CSP. There are three Datalog fragments that are particularly important for…
We present a hierarchy of tractable relaxations to obtain lower bounds on the minimum value of a polynomial over a constraint set defined by polynomial equations. In contrast to previous convex relaxation techniques for this problem, our…
Seeking tighter relaxations of combinatorial optimization problems, semidefinite programming is a generalization of linear programming that offers better bounds and is still polynomially solvable. Yet, in practice, a semidefinite program is…
Constraint satisfaction problems (CSPs) are about finding values of variables that satisfy the given constraints. We show that Transformer extended with recurrence is a viable approach to learning to solve CSPs in an end-to-end manner,…
Mathematical Programs with Vanishing Constraints (MPVCs) are a notoriously challenging class of problems owing to their lack of constraint qualification. Therefore, to tackle these problems, relaxation-based approaches are typically used.…
The so-called algebraic approach to the constraint satisfaction problem (CSP) has been a prevalent method of the study of complexity of these problems since early 2000's. The core of this approach is the notion of polymorphisms which…
Separable convex optimization problems with linear ascending inequality and equality constraints are addressed in this paper. Under an ordering condition on the slopes of the functions at the origin, an algorithm that determines the optimum…
Constraint Programming (CP) solvers typically tackle optimization problems by repeatedly finding solutions to a problem while placing tighter and tighter bounds on the solution cost. This approach is somewhat naive, especially for…
The Promise Constraint Satisfaction Problem (PCSP) is a generalization of the Constraint Satisfaction Problem (CSP) that includes approximation variants of satisfiability and graph coloring problems. Barto [LICS '19] has shown that a…