We consider optimization problems with equality, inequality, and abstract set constraints, and we explore various characteristics of the constraint set that imply the existence of Lagrange multipliers. We prove a generalized version of the Fritz-John theorem, and we introduce new and general conditions that extend and unify the major constraint qualifications. Among these conditions, two new pr...

The paper concerns parameter dependent nonlinear optimal control problems, subject to state constraints of the first order. In recent papers of the author (see [1, 2, 3, 4]), weakened conditions are derived, under which the solutions and Lagrange multipliers of the problems are locally Lipschitz continuous and directionally differentiable functions of the parameter. The conditions consist of st...

To get positive Lagrange multipliers associated with each of the objective function, Maeda [Constraint qualification in multiobjective optimization problems: Differentiable case, J. Optimization Theory Appl., 80, 483–500 (1994)], gave some special sets and derived some generalized regularity conditions for first-order Karush–Kuhn– Tucker (KKT)-type necessary conditions of multiobjective optimiz...

This paper proposes low-complexity blind detection for orthogonal frequency division multiplexing (OFDM) systems with the differential space-time block code (DSTBC) under time-varying frequencyselective Rayleigh fading. The detector employs the maximum likelihood sequence estimation (MLSE) in cooperation with the blind linear prediction (BLP), of which prediction coefficients are determined by ...

Connections between Tsallis' formalisms employing the standard linear average energy and ones employing the normalized q-average energy Abstract Tsallis' thermostatistics with the standard linear average energy is revisited by employing S 2−q , which is the Tsallis entropy with q replaced by 2 − q. We explore the connections among the S 2−q approach and the other different versions of Tsal-lis ...

Starting from second-order conditions for C scalar unconstrained optimization problems described in terms of the second-order Dini directional derivative, we pose the problem, whether similar conditions for C vector optimization problems can be derived. We define second-order Dini directional derivatives for vector functions and apply them to formulate such conditions as a Conjecture. The proof...

In this paper we deal with the perceptually motivated signal subspace methods for speech enhancement. We focus on extended spectral-domain-constrained (SDC) estimator. It is obtained using Lagrange multipliers method. We present an algorithm for a precise computation of the Lagrange multipliers, allowing for a direct shaping the residual noise power spectrum. In addition the SDC estimator is pr...

A three-level domain decomposition is considered. Bodies in contact with each other are divided into subdomains, which in turn are the union of elements. Using an approach based purely on FETI (finite element tearing and interconnecting) algorithms with only Lagrange multipliers as unknowns, which has been developed by the engineering community, does not lead to a scalable algorithm with respec...

We consider optimization problems with equality, inequality, and abstract set constraints, and we explore various characteristics of the constraint set that imply the existence of Lagrange multipliers. We prove a generalized version of the Fritz-John theorem, and we introduce new and general conditions that extend and unify the major constraint qualifications. Among these conditions, two new pr...