We study the convergence of general abstract descent methods applied to a lower semicontinuous nonconvex function f that satisfies the KurdykaLojasiewicz inequality in a Hilbert space. We prove that any precompact sequence converges to a critical point of f and obtain new convergence rates both for the values and the iterates. The analysis covers alternating versions of the forward-backward met...

We study the convergence of general abstract descent methods applied to a lower semicontinuous nonconvex function f that satisfies the KurdykaLojasiewicz inequality in a Hilbert space. We prove that any precompact sequence converges to a critical point of f and obtain new convergence rates both for the values and the iterates. The analysis covers alternating versions of the forward-backward met...

We have explored educational methods for algorithmic thinking for novices and implemented a block programming editor and a simple learning management system. In this paper, we propose a program/algorithm complexity metric specified for novice learners. This metric is based on the variable usage in arithmetic and relational formulas in learner’s algorithms. To evaluate the applicability of this ...

We consider a regularization proximal method with variable metric to solve the nonlinear complementarity problem (NCP ) for P0functions. We establish global convergence properties when the solution set is non empty and bounded. Furthermore, we prove, without boundedness of the solution set, that the sequence generated by the algorithm is a minimizing sequence for the implicit Lagrangian functio...

Computational notions of entropy have recently found many applications, including leakageresilient cryptography, deterministic encryption or memory delegation. The two main types of results which make computational notions so useful are (1) Chain rules, which quantify by how much the computational entropy of a variable decreases if conditioned on some other variable (2) Transformations, which q...

this paper addresses the design of control charts for both variable ( x chart) andattribute (u and c charts) quality characteristics, when there is uncertainty about the processparameters or sample data. derived control charts are more flexible than the strict crisp case, dueto the ability of encompassing the effects of vagueness in form of the degree of expert’spresumption. we extend the use o...

We investigate how information leakage reduces computational entropy of a random variable X. Recall that HILL and metric computational entropy are parameterized by quality (how distinguishable is X from a variable Z that has true entropy) and quantity (how much true entropy is there in Z). We prove an intuitively natural result: conditioning on an event of probability p reduces the quality of m...

We investigate how information leakage reduces computational entropy of a random variable X. Recall that HILL and metric computational entropy are parameterized by quality (how distinguishable is X from a variable Z that has true entropy) and quantity (how much true entropy is there in Z). We prove an intuitively natural result: conditioning on an event of probability p reduces the quality of m...