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The CLP scheme uses Horn clauses and SLD resolution to generate multiple constraint satisfaction problems (CSPs). The possible CSPs include rational trees (giving Prolog) and numerical algorithms for solving linear equations and linear…
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…
In this paper, we provide conditions under which one can take derivatives of the solution to convex optimization problems with respect to problem data. These conditions are (roughly) that Slater's condition holds, the functions involved are…
In the article \The State of SAT", the authors asked whether a procedure dramatically different from DPLL can be found for handling unsatisfiable instances. This study proposes a new linear programming approach to address this issue…
We study optimal decision policies for integer linear programs with a fixed feasible set and varying cost vectors, represented as linear decision trees. Once synthesized for a given feasible set, they return an optimal solution for any…
We consider a general linear program in standard form whose right-hand side constraint vector is subject to random perturbations. This defines a stochastic linear program for which, under general conditions, we characterize the fluctuations…
We introduce a novel kind of robustness in linear programming. A solution x* is called robust optimal if for all realizations of objective functions coefficients and constraint matrix entries from given interval domains there are…
We propose an algorithm for solving bound-constrained mathematical programs with complementarity constraints on the variables. Each iteration of the algorithm involves solving a linear program with complementarity constraints in order to…
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…
Strong (Lagrangian) duality of general conic optimization problems (COPs) has long been studied and its profound and complicated results appear in different forms in a wide range of literatures. As a result, characterizing the known and…
We introduce and study the infinite dimensional linear programming problem which along with its dual allows one to characterize the optimal value of the deterministic long-run average optimal control problem in the general case when the…
This note establishes a limiting formula for the conic Lagrangian dual of a convex infinite optimization problem, correcting the classical version of Karney [Math. Programming 27 (1983) 75-82] for convex semi-infinite programs. A…
Discrete-time robust optimal control problems generally take a min-max structure over continuous variable spaces, which can be difficult to solve in practice. In this paper, we extend the class of such problems that can be solved through a…
Many logic programming based approaches can be used to describe and solve combinatorial search problems. On the one hand there are definite programs and constraint logic programs that compute a solution as an answer substitution to a query…
We consider the convex bilevel optimization problem, also known as simple bilevel programming. There are two challenges in solving convex bilevel optimization problems. Firstly, strong duality is not guaranteed due to the lack of Slater…
We prove the existence of explicit linear multistep methods of any order with positive coefficients. Our approach is based on formulating a linear programming problem and establishing infeasibility of the dual problem. This yields a number…
This paper investigates the relation between sequential convex programming (SCP) as, e.g., defined in [24] and DC (difference of two convex functions) programming. We first present an SCP algorithm for solving nonlinear optimization…
In Constraint Programming, solving discrete minimization problems with hard and soft constraints can be done either using (i) soft global constraints, (ii) a reformulation into a linear program, or (iii) a reformulation into local cost…
We consider infinite horizon optimal control problems with time averaging and time discounting criteria and give estimates for the Cesaro and Abel limits of their optimal values in the case when they depend on the initial conditions. We…
We give an approximation algorithm for packing and covering linear programs (linear programs with non-negative coefficients). Given a constraint matrix with n non-zeros, r rows, and c columns, the algorithm computes feasible primal and dual…