The generation of piecewise linear maps has received a lot of attention from the scientific community. In particular, locally injective maps are very important in many fields, from geometry processing and shape modelling to computer games and movies. We propose a mesh-based method for computing positionally constrained piece-wise linear maps which are locally injective and have low distortion. ...

Abstract In this paper, we present a majorized semismooth Newton-CG augmented Lagrangian method, called SDPNAL+, for semidefinite programming (SDP) with partial or full nonnegative constraints on the matrix variable. SDPNAL+ is a much enhanced version of SDPNAL introduced by Zhao et al. (SIAM J Optim 20:1737–1765, 2010) for solving generic SDPs. SDPNAL works very efficiently for nondegenerate S...

Based on the classic augmented Lagrangian multiplier method, we propose, analyze and test an algorithm for solving a class of equality-constrained nonsmooth optimization problems (chiefly but not necessarily convex programs) with a particular structure. The algorithm effectively combines an alternating direction technique with a nonmonotone line search to minimize the augmented Lagrangian funct...

This paper presents an enhanced merit order (EMO) and augmented Lagrange Hopfield network (ALHN) for unit commitment (UC). The EMO method is a merit order based heuristic search for unit scheduling and ALHN is a continuous Hopfield network based on augmented Lagrange relaxation for economic dispatch problem. First, generating units are sorted in ascending average production cost and committed t...

This paper presents an augmented Lagrangian algorithm to solve continuous constrained global optimization problems. The algorithm approximately solves a sequence of bound constrained subproblems whose objective function penalizes equality and inequality constraints violation and depends on the Lagrange multiplier vectors and a penalty parameter. Each subproblem is solved by a population-based m...

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 propose a new first-order augmented Lagrangian algorithm ALCC for solving convex conic programs of the form min { ρ(x) + γ(x) : Ax− b ∈ K, x ∈ χ } , where ρ : Rn → R ∪ {+∞}, γ : Rn → R are closed, convex functions, and γ has a Lipschitz continuous gradient, A ∈ Rm×n, K ⊂ Rm is a closed convex cone, and χ ⊂ dom(ρ) is a “simple” convex compact set such that optimization problems of the form mi...