and Applied Analysis 3 Given x, λ, μ, c , the augmented Lagrangian relaxation problem associated with the augmented Lagrangian L is defined by min L ( x, λ, μ, c ) s.t. x ∈ Ω. Lλ,μ,c Given ε ≥ 0, then the ε-optimal solution set of Lλ,μ,c , denoted by S∗ λ, μ, c, ε , is defined as { x ∈ Ω | Lx, λ, μ, c ≤ inf x∈Ω L ( x, λ, μ, c ) ε } . 2.2 IfΩ is closed and bounded, then the global optimal soluti...

We show improved NP-hardness of approximating Ordering Constraint Satisfaction Problems (OCSPs). For the two most well-studied OCSPs, MAXIMUM ACYCLIC SUBGRAPH and MAXIMUM BETWEENNESS, we prove NP-hard approximation factors of 14 15 + ε and 1 2 + ε . When it is hard to approximate an OCSP by a constant better than taking a uniformly-at-random ordering, then the OCSP is said to be approximation r...

A highly competitive micro evolutionary algorithm to solve unconstrained optimization problems called μJADE (micro adaptive differential evolution), is adapted to deal with constrained search spaces. Two constraint-handling techniques (the feasibility rules and the ε-constrained method) are tested in μJADE and their performance is analyzed. The most competitive version is then compared against ...

This work is concerned with approximating constraint satisfaction problems (CSPs) with an additional global cardinality constraints. For example, Max Cut is a boolean CSP where the input is a graph G = (V, E) and the goal is to find a cut S ∪ S̄ = V that maximizes the number of crossing edges, |E(S , S̄ )|. The Max Bisection problem is a variant of Max Cut with an additional global constraint tha...

Abstract. To deal with the divergence-free constraint in a double curl problem: curlμ−1curlu = f and div εu = 0 in Ω, where μ and ε represent the physical properties of the materials occupying Ω, we develop a δ-regularization method: curlμcurluδ + δεuδ = f to completely ignore the divergence-free constraint div εu = 0. It is shown that uδ converges to u in H(curl ; Ω) norm as δ → 0. The edge fi...

We consider the problem of solving packing/covering LPs online, when the columns of the constraint matrix are presented in random order. This problem has received much attention: the main open question is to figure out how large the right-hand sides of the LPs have to be (compared to the entries on the left-hand side of the constraint) to get (1 + ε)-approximations online? It is known that the ...

This paper describes an exact ε-constraint method for bi-objective combinatorial optimization problems with integer objective values. This method tackles multi-objective optimization problems by solving a series of single objective subproblems, where all but one objective are transformed into constraints. We show in this paper that the Pareto front of bi-objective problems can be efficiently ge...