We study in this paper the strong duality for discrete-time convex constrained portfolio selection problems when adopting a risk neutral computational approach. In contrast to the continuous-time models, there is no known result of the existence conditions in discrete-time models to ensure the strong duality. Investigating the relationship among the primal problem, the Lagrangian dual and the P...

In the previous lecture, in the first place, we talked about duality for general non-convex optimization. And we know that dual functions are always convex. The dual of the dual problem is also convex. In applications, the dual of the dual can be used as the convex relaxation of the primal (and we will see this explicitly in the next lecture). Then, we covered the concepts of weak duality and s...

Objective: This study aims to find and compare the effects of primal reflex release technique and stretching exercises on pain intensity, functional performance, and pain-free sitting duration in patients with coccydynia. Methods: This is a randomized clinical trial. A total of 46 individuals were chosen for the sample based on the inclusion criteria, and they were divided into groups A and B....

We study monotonicity of primal and dual objective values in the framework of primal-dual interior-point methods. The primal-dual aane-scaling algorithm is monotone in both objectives. We derive a condition under which a primal-dualinterior-point algorithm with a centering component is monotone. Then we propose primal-dual algorithms that are monotone in both primal and dual objective values an...

In this paper, we study polynomial-time interior-point algorithms in view of information geometry. Information geometry is a differential geometric framework which has been successfully applied to statistics, learning theory, signal processing etc. We consider information geometric structure for conic linear programs introduced by self-concordant barrier functions, and develop a precise iterati...

Motivated by various applications to computer vision, we consider the convex cost tension problem, which is the dual of the convex cost flow problem. In this paper, we first propose a primal algorithm for computing an optimal solution of the problem. Our primal algorithm iteratively updates primal variables by solving associated minimum cut problems. We show that the time complexity of the prim...

Using theorem prover Coq [4] for the verification of concurrent systems usually includes the formalization of the modal μ–calculus [8] in that logical framework [13] [11] [15]. These implementations build upon the following interpretation: given the state space S of a system, the meaning of a formula is the subset of states where it is satisfied. Then, a formula α(X) with a free variable X can ...

A type system for the lambda-calculus enriched with recursive and corecursive functions over equi-inductive and -coinductive types is presented in which all well-typed programs are strongly normalizing. The choice of equi-inductive types, instead of the more common isoinductive types, in uences both reduction rules and the strong normalization proof. By embedding isointo equi-types, the latter ...