(1 < p ≤ ∞) [LS87f]. (2) [HR88a]. (2m− 2) [KL88]. (A0, A1)θ1 [Xu87a]. (α, β) [Pie88a, Fin88a]. (d ≥ 1) [Wsc85a]. (λ) [DM85b]. (Z/2) [Car86b]. (nα) [Sch85h]. (φ)2 [BM89c]. (τ − λ)u = f [Wei87r]. (x, t) [Lum87, Lum89]. (X1 −X3, X2 −X3) [SW87]. 0 [Caz88, Kas86, Pro87]. 0 < p < 1 [Cle87]. 1 [Bak85a, DD85, Drm87, Eli88, FT88a, Gek86d, HN88, Kos86a, LT89, Pet89a, Pro87, Tan87, vdG89]. 1/4 [KS86e]. 1 ≤ q < 2 [Gue86]. 2 [BPPS87, Cam88, Cat85a, ES87b, Gan85e, Gol86a, HRL89g, Hei85, Hua86, Kan89, KB86, Li86, LT89, Mil87b, Mur85a, Qui85b, SP89, Shi85, Spe86, Wal85b, Wan86]. 2m− 2 [Kos88b]. 2m− 3 [Kos88b]. 2m− 4 [Kos88b]. 2× 2 [Vog88]. 3 [Aso89, BPPS87, BW85c, BG88b, Che86d, Fis86, Gab85, Gu87a, HLM85b, Kam89b, Kir89c, Lev85c, Mil85c, Néd86, Pet86, Ron86, Sch85b, ST88, Tur88b, Wan86, Wen85, tDP89, vdW86]. 4 [Bau88a, Don85a, FKV88, Kha88, Kir89l, SS86, Seg85b, Wal85b]. 5 [Ito89, Kir89e, SV85]. 5(4) [Cas86]. 5819539783680 [KSX87]. 6 [PH89, Žub88].

/pdf/a-complete-bibliography-of-lecture-notes-in-mathematics-1985-32lbz48rms.pdf

A Complete Bibliography of Lecture Notes in Mathematics (1985{1989)

In this tutorial survey we study finite dimensional optimization problems which depend on parameters. It is our aim to work out several basic connections with different mathematical areas. In particular, attention will be paid to unfolding and singularity theory, structural analysis of families of constraint sets, constrained optimization problems and semi-infinite optimization.

On parametric nonlinear programming

An implicit-function theorem for C0, 1-equations and parametric C1, 1-optimization

The global resolution of constrained non-linear bi-objective optimization problems (NLBOO) aims at covering their Pareto-optimal front which is in general a one-manifold in $$\mathbb {R}^2$$R2. Continuation methods can help in this context as they can follow a continuous component of this front once an initial point on it is provided. They constitute somehow a generalization of the classical scalarization framework which transforms the bi-objective problem into a parametric single-objective problem. Recent works have shown that they can play a key role in global algorithms dedicated to bi-objective problems, e.g. population based algorithms, where they allow discovering large portions of locally Pareto optimal vectors, which turns out to strongly support diversification. The contribution of this paper is twofold: we first provide a survey on continuation techniques in global optimization methods for NLBOO, identifying relations between several work and usual limitations, among which the ability to handle inequality constraints. We then propose a rigorous active set management strategy on top of a continuation method based on interval analysis, certified with respect to feasibility, local optimality and connectivity. This allows overcoming the latter limitation as illustrated on a representative bi-objective problem.

/pdf/on-continuation-methods-for-non-linear-bi-objective-470zklt5ql.pdf

On continuation methods for non-linear bi-objective optimization: towards a certified interval-based approach

https://hal.archives-ouvertes.fr/hal-02067415/document

A multi-parametric recursive continuation method for nonlinear dynamical systems

We consider finite dimensional optimization problems depending on one real parameter t Recently, Jongen/Jonker/Twilt [9] studied the generic behaviour of such problems Based on this investigation, we propose a partial concept for finding a suitably fine discretization 0=to<…<ti−1<ti<…<tN=1 of the interval [0,1], and corresponding local minima x(ti), i=1,…,N; here, information on the point x(ti-1) is used in order to compute x(ti) Mainly, socalled continuation methods can be exploited However, at some parameter values, the branch of local minima used might have an endpoint; at such points one has to jump to another branch of local minima in order to continue the execution of the desired process In case that the feasible set in a neighborhood of such a mentioned endpoint remains nonempty for increasing parameter values, it will be shown how a jump can be realized

Hubertus Th. Jongen

Papers

Parametric optimization: Pathfollowing with jumps