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Sequential Constant Rank Constraint Qualifications for Nonlinear Semidefinite Programming with Algorithmic Applications
We present new constraint qualification conditions for nonlinear semidefinite programming that extend some of the constant rank-type conditions from...
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On the Weak Second-order Optimality Condition for Nonlinear Semidefinite and Second-order Cone Programming
Second-order necessary optimality conditions for nonlinear conic programming problems that depend on a single Lagrange multiplier are usually built...
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A Nonmonotone Smoothing Newton Method for Systems of Nonlinear Equalities and Inequalities Based on a New Smoothing Function
In this paper, a nonmonotone smoothing Newton method is proposed for solving systems of non-linear equalities and inequalities. By constructing a new...
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Nonlinear Forward-Backward Splitting with Momentum Correction
The nonlinear, or warped, resolvent recently explored by Giselsson and Bùi-Combettes has been used to model a large set of existing and new monotone...
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A Projective Sequential Adaptive Cubic Regularisation Algorithm for Constrained Optimization
A projective sequential adaptive regularization algorithm using cubics (ARC) with line search filter techniques is presented to solve nonlinear...
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Convergence of an augmented Lagrange algorithm for nonlinear optimizations with second-order cone constraints
An augmented Lagrange algorithm for nonlinear optimizations with second-order cone constraints is proposed based on a Löwner operator associated with...
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A flexible objective-constraint approach and a new algorithm for constructing the Pareto front of multiobjective optimization problems
In this article, a novel scalarization technique, called the improved objective-constraint approach, is introduced to find efficient solutions of a...
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Estimates of Generalized Hessians for Optimal Value Functions in Mathematical Programming
We consider the optimal value function of a parametric optimization problem. A large number of publications have been dedicated to the study of...
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A New QP-free Algorithm Without a Penalty Function or a Filter for Nonlinear Semidefinite Programming
In this paper, we present a QP-free algorithm without a penalty function or a filter for nonlinear semideflnite programming. At each iteration, two...
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Local Near-Quadratic Convergence of Riemannian Interior Point Methods
We consider Riemannian optimization problems with inequality and equality constraints and analyze a class of Riemannian interior point methods for...
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\({\cal U}{\cal V}\)-theory of a Class of Semidefinite Programming and Its Applications
In this paper we study optimization problems involving convex nonlinear semidefinite programming (CSDP). Here we convert CSDP into eigenvalue problem...
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A new diagonal quasi-Newton algorithm for unconstrained optimization problems
We present a new diagonal quasi-Newton method for solving unconstrained optimization problems based on the weak secant equation. To control the...
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Semi-infinite interval-valued optimization problems with robust constraints
In this paper, we consider a robust semi-infinite interval-valued optimization problem with inequality constraints having an uncertain parameter. The...
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Variational Analysis of a Nonconvex and Nonsmooth Optimization Problem: An Introduction
Variational analysis provides the theoretical foundations and practical tools for constructing optimization algorithms without being restricted to...
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A Constant Rank Constraint Qualification in Continuous-Time Nonlinear Programming
The paper addresses continuous-time nonlinear programming problems with equality and inequality constraints. First and second order necessary...
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Two Nonmonotone Proximal Gradient Methods for Nonsmooth Optimization over the Stiefel Manifold
We propose two nonmonotone retraction-based proximal gradient methods for solving a class of nonconvex nonsmooth optimization problems over the...
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Global convergence of a cautious projection BFGS algorithm for nonconvex problems without gradient Lipschitz continuity
A cautious projection BFGS method is proposed for solving nonconvex unconstrained optimization problems. The global convergence of this method as...
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Sequential M-Stationarity Conditions for General Optimization Problems
In this paper, we investigate sequential M-stationarity conditions for a class of nonsmooth nonconvex general optimization problems. We introduce...
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Variational Analysis of Norm Cones in Finite Dimensional Euclidean Spaces
A norm cone in a finite dimensional Euclidean space is the epigraph of a norm. Many important practical optimization problems are formulated as norm...
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Approximate Stationarity in Disjunctive Optimization: Concepts, Qualification Conditions, and Application to MPCCs
In this paper, we are concerned with stationarity conditions and qualification conditions for optimization problems with disjunctive constraints....