/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

Introduction to linear and nonlinear programming

Remaining useful life estimation - A review on the statistical data driven approaches

A survey of maintenance policies of deteriorating systems

/pdf/sequencing-and-scheduling-algorithms-and-complexity-lnutyrr3kz.pdf

Sequencing and scheduling: algorithms and complexity

An alternative smoothing method for the high dimensional max functionhas been studied. The proposed method is a recursive extension of thetwo dimensional smoothing functions. In order to analyze the proposedmethod, a theoretical framework related to smoothing methods has beendiscussed. Moreover, we support our discussion by considering someapplication areas. This is followed by a comparison with analternative well-known smoothing method.

Recursive Approximation of the High Dimensional Max Function

A probabilistic analysis is presented of the Next Fit Decreasing bin packing heuristic, in which bins are opened to accomodate the items in order of decreasing size.

A probabilistic analysis of the next fit decreasing bin packing heuristic

In this paper portfolio problems with linear loss functions and multivariate elliptical distributed returns are studied. We consider two risk measures, Value-at-Risk and Conditional-Value-at-Risk, and two types of decision makers, risk neutral and risk averse. For Value-at-Risk, we show that the optimal solution does not change with the type of decision maker. However, this observation is not true for Conditional-Value-at-Risk. We then show for Conditional-Value-at-Risk that the objective function can be approximated by Monte Carlo simulation using only a univariate distribution. To solve the equivalent Markowitz model, we modify and implement a finite step algorithm. Finally, a numerical study is conducted.

https://papers.ssrn.com/sol3/Delivery.cfm/10151.pdf?abstractid=988843&mirid=3

Application of a General Risk Management Model to Portfolio Optimization Problems with Elliptical Distributed Returns for Risk Neutral and Risk Averse Decision Makers

textIn this chapter we give an overview on the theory of noncooperative games. In the first part we consider in detail for zero-sum (and constant-sum) noncooperative games under which necessary and sufficient conditions on the payoff function and different (extended) strategy sets for both players an equilibrium saddlepoint exists. This is done by using the most elementary proofs. One proof uses the separation result for disjoint convex sets, while the other proof uses linear programming duality and some elementary properties of compact sets. Also, for the most famous saddlepoint result given by Sion's minmax theorem an elementary proof using only the definition of connectedness is given. In the final part we consider n-person nonzero-sum noncooperative games and show by a simple application of the KKM lemma that a so-called Nash equilibrium point exists for compact strategy sets and concavity conditions on the payoff functions.

/pdf/on-noncooperative-games-minimax-theorems-and-equilibrium-s10757wt0x.pdf

On Noncooperative Games, Minimax Theorems and Equilibrium Problems

In this note we give an elementary proof of the Fritz-John and Karush-Kuhn-Tucker conditions for nonlinear finite dimensional programming problems with equality and/or inequality constraints. The proof avoids the implicit function theorem usually applied when dealing with equality constraints and uses a generalization of Farkas lemma and the Bolzano-Weierstrass property for compact sets.

/pdf/an-elementary-proof-of-the-fritz-john-and-karush-kuhn-tucker-3z9wu8qp0z.pdf

J. B. G. Frenk

Papers

Recursive Approximation of the High Dimensional Max Function

A probabilistic analysis of the next fit decreasing bin packing heuristic

Application of a General Risk Management Model to Portfolio Optimization Problems with Elliptical Distributed Returns for Risk Neutral and Risk Averse Decision Makers

On Noncooperative Games, Minimax Theorems and Equilibrium Problems

An elementary proof of the Fritz-John and Karush-Kuhn-Tucker conditions in nonlinear programming